These days, TOS is generally treated as covering roughly a 4 year period, instead of three, or at least as covering the middle 3 years of the 5YM instead of the first three. TAS gets shoehorned in at the end of it, and the novels representing the era you're asking about tend to get shuffled in kinda willy nilly.
There's also the "problem" of several books and comics each taking place immediately or shortly after "Turnabout Intruder", representing the end of the 5YM. The Lost Years
and DC Comics' "Final Mission" are two examples, but both great stories in and of themselves.
Really, the best thing to do is to pick up a TOS novel that seems interesting to you, or pretty much any of the DC comics with the crew in their TOS uniforms, and not try to find one specifically set at the end of the 5YM.
That being said, Prime Directive
is a good one, as are Assignment: Eternity
and the aforementioned The Rings of Time
It's easier to pinpoint books set between TMP and TWOK, or between TFF and TUC.