Answer: yes. That's not a fifth amendment issue.
On what are you basing your answer? Because I'm thinking of the "link in the chain" doctrine,
see Hoffman v. United States, 341 U.S. 479, 486 (1951), which holds that the 5th Amendment privilege applies when the answer to a question might "furnish a link in the chain of evidence" against that person.
In
United States v. Hubbell , 530 U.S. 27 (2000), the Court explained that although being compelled to turn over incriminating material does not implicate the 5th Amendment (because
creation of the material was not compelled), the "the act of producing documents in response to a subpoena may have a compelled testimonial aspect" and therefore be subject to the 5th Amendment because the mere act of production communicates implied statements of fact ("I know what these documents are, they are in my possession, and they are authentic").
Now, it's different with a cell phone (or any computer) because we're not talking about turning over physical pages but only an unlock code. I can see how that distinction MIGHT change the answer, but it seems to me a debatable point -- unless you know something I don't?
Wikipedia (for what that's worth) also indicates that there is no unanimity in the courts on this point:
Computer passwords[edit]
Courts have given conflicting decisions on whether forced disclosure of computer passwords is a violation of the Fifth Amendment.
In In re Boucher (2009), the US District Court of Vermont ruled that the Fifth Amendment might protect a defendant from having to reveal an encryption password, or even the existence of one, if the production of that password could be deemed a self-incriminating "act" under the Fifth Amendment. In Boucher, production of the unencrypted drive was deemed not to be a self-incriminating act, as the government already had sufficient evidence to tie the encrypted data to the defendant.[69]
In January 2012 a federal judge in Denver ruled that a bank-fraud suspect was required to give an unencrypted copy of a laptop hard drive to prosecutors.[70][71] However, in February 2012 the Eleventh Circuit ruled otherwise - finding that requiring a defendant to produce an encrypted drive's password would violate the Constitution, becoming the first federal circuit court to rule on the issue.[72][73] In April 2013, a District Court magistrate judge in Wisconsin refused to compel a suspect to provide the encryption password to his hard drive after FBI agents had unsuccessfully spent months trying to decrypt the data.[74][75]
If you're aware of current case law resolving this issue definitively, I'd be very interested to read it!
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Then the suspect is going to jail until they do unlock it and the data is irrelevant.
I wouldn't say it's irrelevant, even if they sit in jail indefinitely. There's a difference, legally speaking, and to us as a society, between a person sitting in jail indefinitely for refusing to comply with a court order, and a person being convicted of <insert terrible crime here> because police found evidence of <terrible crime> sufficient to convict them.
Yes, the end result may look the same -- defendant sitting in jail -- but I don't think we as a society should view those two outcomes as equivalent, and I certainly don't think the victim of a crime (who never gets to see the defendant tried and convicted for the offense charged) would see them as equivalent.
In the first case, you'd undoubtably have people who viewed the defendant as a martyr of sorts, standing up for privacy. Moreover, he'd never be a convicted felon, with its attendant stigma, and the victims would never have the vindication of testifying, making an impact statement, and having a judge or jury saying "you, sir, are found guilty beyond a reasonable doubt of <committing terrible crime>."
