In my mind the fifth year Kirk refers to in "Bread and Circuses" was a year of command school after the standard four year training at the Academy. You could take it directly after you graduate or come back and take it later if you wish to command a ship someday.
That doesn't seem to account for Merik, though. If he had graduated he could still have a Starfleet career without the command school. The implication was that he hadn't completed SA and was out. Not to mention that it would be odd to send officers with no fleet experience directly to command shcool.
Which explains why Saavik and Kirk(s) were at the Academy while holding the rank of Lieutenant.
I'm not sure what the Kirk reference is, probably something I've forgotten. I'm not sure Lt Saavik was associated with the academy in TWOK. She was on a training cruise that also involved cadets, but I don't think there's anything in the movie to suggest she was assigned to SA.