5th amendment is self-incrimination, 4th is unwarranted search and seizure.
I don't know the current law, but it used to be that e-mails left on a server for more than 6 months were treated like abandoned property, which has a lower-bar to clear for the 4th amendment. I seem to recall hearing that this was changed a while back though.
How the 4th amendment applies to any case is complicated though because it's very much a sliding scale of intrusiveness, with higher levels of intrusiveness requiring more cause for searching.
5th amendment is self-incrimination, 4th is unwarranted search and seizure.
I don't know the current law, but it used to be that e-mails left on a server for more than 6 months were treated like abandoned property, which has a lower-bar to clear for the 4th amendment. I seem to recall hearing that this was changed a while back though.
How the 4th amendment applies to any case is complicated though because it's very much a sliding scale of intrusiveness, with higher levels of intrusiveness requiring more cause for searching.