The Government already has a warrant; so the Fourth Amendment is satisfied. The question in this case is whether the Government can compel Apple to help them execute the warrant.
There's some interesting case law around locked things. One train of thought is that the govt can force you to give the key to a safe, but can't force you to give the combination to a safe.
The Apple extension would be that the govt can force unlocking by Apple (since they have a key) but not by you. All the more you reason to make it technically impossible ...
The fifth amendment doesn't apply. This isn't self-incrimination.
As to whether the fourth amendment applies - that's the question they're answering in court. Is this a search, in which case the government can compel Apple to disclose useful information, or is the DoJ asking for Apple to do something on their behalf?