Re: The characters and universe post-TOS
Quite possibly there never was another five-year mission in the history of Starfleet, much less in the history of the Enterprise. At least such things are never referred to in the aired episodes and movies, and the very concept of an X-year mission really only exists in the opening credits of TOS.
Well, in The Menagerie, Part I
, Spock reveals how long he served with Pike--which was far longer than 5 years. Whether his stated number was simply adding up a number of five-year missions, or missions were extended in Pike's active years is unknown, but Spock's line could suggest Starfleet vessels did not all follow the 5-year period of service.
"...to be like God, you have the power to make the world anything you want it to be."