I think many of the Watergate convictions were for perjury long after the fact and not for the initial crimes. Can a person plead the fifth for a crime which is past the limitation? I don't know.
IANAL (I am not a lawyer) but my understanding is you can plead the 5th anytime you want. However it is usually viewed as an admission of guilt, and typically results in an increase of investigatory powers being used against you to uncover whatever it is that you don't want to discuss. And the more investigatory powers that were used, those came at a cost of resources, therefore they are more likely to throw the book at you if/when they find something. Sort of the exact opposite of a "no contest" plea to a court, where you are throwing yourself at the mercy of the court, essentially pleading guilty, but hoping to get a reduced sentence since the court isn't going to have to expend any resources on the case.