
646 F.3d 1012 (2011)
UNITED STATES of America, Plaintiff-Appellee,
v.
Donald G. BRUCKER, Defendant-Appellant.
No. 10-3057.
United States Court of Appeals, Seventh Circuit.
Argued February 9, 2011.
Decided July 22, 2011.
*1014 Thomas A. Keith, Attorney, Office of the United States Attorney, Peoria, IL, Linda L. Mullen (argued), Attorney, Office of the United States Attorney, Rock Island, IL, for Plaintiff-Appellee.
James A. Martinkus (argued), Attorney, Erwin, Martinkus & Cole, Champaign, IL, for Defendant-Appellant.
Before EASTERBROOK, Chief Judge, and FLAUM and RIPPLE, Circuit Judges.
RIPPLE, Circuit Judge.
Donald Brucker pleaded guilty to one count of attempting to entice a minor to engage in sexual activity, in violation of 18 U.S.C. § 2422(b), and to one count of attempting to transfer obscene material to a minor, in violation of 18 U.S.C. § 1470. Mr. Brucker was sentenced to the statutory minimum sentence of 120 months' imprisonment. He now appeals his sentence. For the reasons set forth in this opinion, we affirm the judgment of the district court.[1]

I

BACKGROUND

A.
In mid-October 2009, Mr. Brucker entered an internet chat room and began communicating with another user, named "Lisa," who identified herself as a fifteen-year-old girl from Peoria, Illinois. During their first conversation, Mr. Brucker asked for photographs of Lisa. After receiving only innocuous photos, he asked her to send some "sexy" ones. R.17 at 6 (quotation marks omitted). Mr. Brucker also made explicit, sexual comments about things he would like to do with Lisa. When Lisa asked Mr. Brucker if he cared that she was only fifteen, he responded that he did not mind as long as she kept it a secret.
Over the course of the next two months, Mr. Brucker continued to contact Lisa online; the conversations were consistently of a sexual nature and included a number of propositions to engage in sexual relations. In late October, Mr. Brucker suggested to Lisa that she arrange for a ride to the Walmart in Morton, Illinois, so that she could meet him in his motel room across the road. He also asked her to get a webcam so that he could see her naked while they chatted. In early December, Mr. Brucker began planning to meet Lisa at a restaurant parking lot near her home. He then planned to drive her in his truck to an isolated and unpatrolled location in the country. During this time, Mr. Brucker also exposed himself to her on more than one occasion, via a live webcam. Mr. Brucker and Lisa finally agreed to meet in the restaurant parking lot on December 14, 2009, in the afternoon.
"Lisa" was in fact an online persona for a deputy in the Peoria County Sheriff's Office. On December 14, after observing Mr. Brucker's car at the prearranged location in the restaurant parking lot and visually identifying him as the man in the webcam videos, the deputy, accompanied by another officer, contacted Mr. Brucker online as "Lisa." Once Mr. Brucker had confirmed that Lisa was on her way to meet him, he entered the restaurant. When Mr. Brucker exited the restaurant, *1015 the officers confronted him. After initially denying any involvement, Mr. Brucker ultimately admitted that he was there to meet a fifteen-year-old girl. In searching his car, the officers recovered a laptop and an unopened package of condoms.
Mr. Brucker was sixty-two years old at the time he committed the offense.

B.
Mr. Brucker was charged in a two-count indictment with attempting to entice a minor to engage in sexual activity and attempting to transfer obscene material to a minor. See 18 U.S.C. §§ 2422(b), 1470. He pleaded guilty to both counts.
At sentencing, Mr. Brucker filed an objection to the presentence investigation report ("PSR"), in which he requested a sentence below the statutory minimum of 120 months. See 18 U.S.C. § 2422(b). In addition, he included more than twenty letters of support and statements regarding his character.
The district court quickly rejected Mr. Brucker's request for a below-minimum sentence and adopted the PSR in its entirety. The court acknowledged that, absent the statutory minimum, the sentencing range for Mr. Brucker under the Guidelines would have been 70-87 months, but it explained that the statutory mandatory minimum of ten years was controlling.
After permitting Mr. Brucker to address the court and hearing argument from the Government's counsel, the district court then turned to the sentencing calculation:
The Court has no real need nor obligation nor is it relevant to discuss Mr. Bru[c]ker's history and characteristics because while that's one of the several sentencing factors the Court looks at in the typical case, . . . which as I've indicated in this case reflect a man who has been a very decent man. But it doesn't matter whether he has or has not. The law is that there is a mandatory minimum of ten years.
R.40 at 22-23. The court noted several reasons for Congress's decision to treat these kinds of cyber-offenses with such severity, including that they target children, that they can be accomplished from the privacy of the offender's home and that troubled children are particularly susceptible to the advances of predators. The court then stated:
[Mr. Brucker] is still the father or grandpa, the friend and neighbor that we have learned to depend upon and love over the years. All that is good and fine but you got to understand my job today is not to look at Mr. Bru[c]ker and put on one side his good works and put on this side this crime. I don't have the power to do that. I'm told I can't do that. I'm told that you must impose a sentence that the people speaking through their representatives have said for this type of crime, this is a punishment for all people. . . .
Id. at 24. The court therefore sentenced Mr. Brucker to 120 months' imprisonment and a fine of $12,500.

II

DISCUSSION
Mr. Brucker presents several constitutional challenges to statutory minimum sentences, for which he relies primarily on the premise that, as a constitutional matter, the legislature cannot remove all discretion from the sentencing judge. He bases these arguments on the Supreme Court's decisions in United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), and Blakely v. Washington, 542 U.S. 296, 124 S.Ct. 2531, 159 L.Ed.2d 403 (2004), as well as on the Equal Protection *1016 Clause of the Fifth Amendment, the proportionality principle of the Eighth Amendment and the doctrine of separation of powers. We review constitutional challenges to a sentence de novo. United States v. Nagel, 559 F.3d 756, 759 (7th Cir.2009).

A.
Mr. Brucker submits that the Supreme Court's decision in Booker has been unduly limited by the Courts of Appeals to its "narrow" remedial holding. Appellant's Br. 10. In his view, Booker incorporated the due process analysis set forth by the Court in Blakely. In so doing, Mr. Brucker asserts, Booker reset the balance between the legislature's prerogative to dictate sentences and the judiciary's obligation to exercise its discretion to ensure that individualized sentences comport with the demands of due process under the Fifth Amendment.
We have stated on numerous occasions that Booker has no effect on statutory minimum sentences, generally in the context of denying a remand under United States v. Paladino, 401 F.3d 471, 483-85 (7th Cir.2005), to defendants who were sentenced to the statutory minimum. See United States v. Douglas, 569 F.3d 635, 636 (7th Cir.2009) (finding an erroneous guidelines calculation harmless because "Booker does not confer on district judges any discretion to give sentences below statutory floors" (quotation marks omitted)); United States v. Lee, 399 F.3d 864, 866 (7th Cir.2005) ("Nothing in Booker gives a judge any discretion to disregard a mandatory minimum. . . ."). Indeed, in United States v. Roberson, 474 F.3d 432, 436-37 (7th Cir.2007), we stated:
We acknowledge the tension with section 3553(a), but that very general statute cannot be understood to authorize courts to sentence below minimums specifically prescribed by Congress. That was the rule when the guidelines were mandatory, and it was not changed by Booker. For in making the sentencing guidelines advisory, the Court did not authorize courts to sentence below the minimums prescribed not by the guidelines but by constitutional federal statutes. Booker has nothing to do with minimum sentences. The judiciary is not free to replace Congress's approach with one that it deems superior.
Id. at 436-37 (internal citations and quotation marks omitted).
Mr. Brucker provides a citation to Kimbrough v. United States, 552 U.S. 85, 128 S.Ct. 558, 169 L.Ed.2d 481 (2007), in support of his argument for mandatory judicial discretion in sentencing, but this case affords him no basis for challenging mandatory minimum sentences. Although the crack-powder disparity exists in both the statute and the Sentencing Guidelines, under Kimbrough, courts are only permitted to depart from the Guidelines based on a policy disagreementnot from the mandatory minimum sentences under the statute. See id. at 107, 128 S.Ct. 558. Indeed, in Kimbrough, the Supreme Court explicitly recognized, post-Booker, that sentencing courts remain bound by mandatory minimums. See id.

B.
Mr. Brucker next raises three distinct equal protection arguments to challenge his sentence. He compares himself (1) to sex offenders covered by the same mandatory minimum statute whose conduct is more serious, (2) to first-time, nonviolent drug offenders, who are covered by the permissive departure, or "safety valve," found in 18 U.S.C. § 3553(f) and (3) to offenders with the same conduct who are prosecuted in Illinois state courts. These challenges arise under the Fifth *1017 Amendment, which "contains an equal protection component." S.F. Arts & Athletics, Inc. v. United States Olympic Comm., 483 U.S. 522, 542 n. 21, 107 S.Ct. 2971, 97 L.Ed.2d 427 (1987). "The approach to Fifth Amendment equal protection claims has been precisely the same as to equal protection claims under the Fourteenth Amendment." Nagel, 559 F.3d at 760 (internal quotation marks omitted). For claims based on either the Fifth or the Fourteenth Amendment, "[e]qual protection of the laws means that all persons similarly situated should be treated alike." Id.
Mr. Brucker acknowledges that his equal protection challenges are all subject to the rational basis test. Under this standard, the statute will be upheld "if there is a rational relationship between the disparity of treatment and some legitimate governmental purpose." Smith v. City of Chicago, 457 F.3d 643, 652 (7th Cir.2006) (emphasis in original) (quotation marks omitted).
Mr. Brucker's first argument with respect to equal protection is that the federal courts have applied § 2422(b) more stringently in cases involving "cyber-offenders" than in cases involving "real-world offenders." Specifically, Mr. Brucker argues that he has been denied equal protection because courts have construed more liberally what constitutes a "substantial step" in an attempt to commit a sex offense against a child when the case involves a cyber-offender. Mr. Brucker asserts that, as a result of this discriminatory standard, a real-world attempt offender may receive a lighter sentence than a cyber-offender.
Mr. Brucker provides no support for his view, that, in some of our cases, we have construed more liberally what constitutes a substantial step in the online context than we have in those cases that have involved a personal encounter. Even if Mr. Brucker's rendition were a complete and accurate assessment of the case law, however, it would be of no assistance to him. In his plea agreement, Mr. Brucker acknowledged, without objection, that the Government could satisfy the substantial step element required for attempt.
Moreover, to the extent that Mr. Brucker argues that the statute lacks a rational basis for treating him the same as (as opposed to worse than) a real-world offender, this argument must fail. Mr. Brucker believed that he had engaged in sexual activity with an actual fifteen-year-old girl, and, therefore, he is equally culpable and poses no less danger to the community based simply on the fact that the actual object of his advances was an undercover officer. In United States v. Nagel, 559 F.3d 756, 764 (7th Cir.2009), we stated: "It is clear that Congress contemplated a mandatory minimum sentence whether there is an actual minor involved or not."
Mr. Brucker's second equal protection argument is that there is no rational basis to support the application of the safety valve provided in § 3553(f) to only drug-related offenses.[2] We considered and rejected squarely this argument in Nagel, which presented factual circumstances nearly identical to Mr. Brucker's case. See id. at 760-62. We identified a number *1018 of rational bases for the distinction between defendants such as Mr. Brucker and criminal defendants who have violated the Controlled Substances Act, including Congress's view about the relative seriousness of the offenses and the fact that the "safety valve" provision was intended to correct what Congress perceived to be a problem with respect to the sentencing of nonviolent drug offenders to overly harsh sentences. See id. at 760-61. By contrast, Congress established the mandatory minimum in § 2422(b) to address its concern that, given the nature of the offense, defendants who violated § 2422(b) were being sentenced too leniently. See id. at 761. We also noted in Nagel that, in contrast to sex offenses, in which the offender typically acts alone, the need to obtain the cooperation of a drug-offense witness, who may have been engaged in a widespread conspiracy, also serves as a rational basis for Congress's decision to treat violators of § 2422(b) more harshly than nonviolent drug offenders. See id.
In his final equal protection argument, Mr. Brucker points out that the state offense on which federal liability is based has no corresponding mandatory minimum.[3] In United States v. Moore, 543 F.3d 891, 897 (7th Cir.2008), we held that "Congress and the state legislatures are free to fashion their own, differing approaches to criminal problems and sentencing" without violating equal protection. "That the federal defendant may face harsher punishment than his state counterpart, or vice versa, simply does not raise equal protection concerns." Id. In an attempt to distinguish this case law, Mr. Brucker argues that Moore held only that each jurisdiction could fashion its own penalties, but did not hold that one jurisdiction could have a mandatory minimum sentence while the other could leave the sentences entirely to the judge's discretion. Mr. Brucker raises a distinction without a difference.

C.
Mr. Brucker contends that the mandatory minimum sentence provision in § 2422(b) violates the Eighth Amendment's prohibition of cruel and unusual punishment, which incorporates a rough proportionality principle.[4]
A sentence must be grossly disproportionate to the crime committed in order to violate the Eighth Amendment's prohibition on cruel and unusual punishment. See Solem v. Helm, 463 U.S. 277, 288, 103 S.Ct. 3001, 77 L.Ed.2d 637 (1983). We therefore begin our inquiry into the circumstances presented by Mr. Brucker's case by evaluating "the gravity of the offense and the harshness of the penalty." Nagel, 559 F.3d at 762 (quotation marks omitted). If this comparison does not lead *1019 us to conclude that Mr. Brucker's is the "rare case" in which an inference of gross disproportionality is raised, our inquiry ends there. Id. (quotation marks omitted). The bar set for evaluating such claims is high. See Harmelin v. Michigan, 501 U.S. 957, 111 S.Ct. 2680, 115 L.Ed.2d 836 (1991) (rejecting a challenge to a mandatory life-without-parole sentence for a first offense involving 672 grams of cocaine); see also Ewing v. California, 538 U.S. 11, 28-31, 123 S.Ct. 1179, 155 L.Ed.2d 108 (2003) (plurality opinion) (affirming a sentence of twenty-five-to-life for felony theft of three golf clubs under the three-strikes rule).
Indeed, in Nagel, we considered and rejected an identical argument:
Employing sexually graphic language, defendant arranged this would-be rendezvous over the Internet, which he also used to send video images of his genitals and anus to the person he thought was a 14-year-old girl. For this he received a ten-year sentence, the statutory minimum. Defendant has not demonstrated how his ten-year sentence for attempting to entice a minor to engage in a criminal sexual act is any more disproportionate than the life sentence without the possibility of parole imposed on a first-time offender for possessing 672 grams of cocaine. Suffice it to say that defendant's sentence is less severe tha[n] the sentence imposed in Harmelin where the Supreme Court rejected an Eighth Amendment proportionality challenge, and does not resemble the life sentence for multiple nonviolent felonies struck down as disproportionate in Solem.

559 F.3d at 763-64 (internal citation omitted).

D.
Finally, Mr. Brucker argues that the legislature exceeds its constitutional authority when it impinges upon the prerogative of the judiciary to impose a sentence that it deems appropriate.
We have rejected separation of powers challenges to mandatory minimum sentences, and we see no reason to revisit that holding here. See United States v. Carraway, 612 F.3d 642, 646-47 (7th Cir.2010) (rejecting the argument that a mandatory life sentence for dealing crack cocaine violates the doctrine of separation of powers as meritless under settled law); see also Harmelin, 501 U.S. at 998, 111 S.Ct. 2680 (Kennedy, J., concurring in part and concurring in the judgment) ("[T]he fixing of prison terms for specific crimes involves a substantive penological judgment that, as a general matter, is properly within the province of legislatures, not courts." (internal quotation marks omitted)).

Conclusion
Mr. Brucker raises no substantial constitutional issue in his attack on mandatory minimum sentences. Accordingly, the judgment of the district court is affirmed.
AFFIRMED
NOTES
[1]  The jurisdiction of the district court was based on 18 U.S.C. § 3231. We have jurisdiction under 28 U.S.C. § 1291 and 18 U.S.C. § 3742.
[2]  Section 3553(f) of Title 18 provides that, in the case of certain offenses under the Controlled Substances Act, when the offender and the offense have certain characteristics, such as the defendant's lack of a criminal history, the offense was committed without violence or threat of violence, no serious injury resulted and the defendant was not an organizer or manager, the district court may sentence the defendant "without regard to any statutory minimum sentence."
[3]  Section 2422(b) makes it a federal crime to use a means of commerce to "knowingly persuade[], induce[], entice[], or coerce[] any individual who has not attained the age of 18 years, to engage in prostitution or any sexual activity for which any person can be charged with a criminal offense." 18 U.S.C. § 2422(b) (emphasis added). The underlying state offense is aggravated criminal sexual abuse. 720 ILCS 5/11-1.60(d).
[4]  Mr. Brucker makes an additional and somewhat related argument that the mandatory minimum sentence violates Woodson v. North Carolina, 428 U.S. 280, 96 S.Ct. 2978, 49 L.Ed.2d 944 (1976), in which the Court invalidated a state statute imposing a mandatory death penalty for first-degree murder. This argument does not merit much discussion as, in the more than thirty years since Woodson was decided, the Court never has cast doubt on the fact that other mandatory minimum sentences were unaffected by its holding. See Lockett v. Ohio, 438 U.S. 586, 604, 98 S.Ct. 2954, 57 L.Ed.2d 973 (1978) (plurality opinion) (noting that Woodson rested on the "qualitative difference" of the death penalty).
