This is also suggested by dialogue in the pilot. I've never liked the idea that WNMHGB was before the 5YM, on some earlier mission or shakedown cruise; I consider it to be the FINALE of an unseen previous season of adventures, that would have had HUGE impact after watching a full set of adventures with Kelso and Mitchell. YMMV. In the old days, I would have loved to see that expressed as a fan series.
I don't see why it can't be both. After all, if 5-year missions aren't a default, that means that missions could come in any number of lengths. They could be brief, single-mission assignments, yeah, or they could be shorter tours of maybe 6 months, a year, 2 years, anything.
The way I portrayed it in The Captain's Oath was that Kirk and the crew had a handful of missions before getting the galaxy-edge assignment (including the first mission in TCO and the missions depicted by Dayton Ward & Kevin Dilmore in SCE: Foundations Book One and Mere Anarchy Book One), and that the trip to the galaxy's edge would've taken long enough that other missions could've happened along the way. My intent was to say that the 5-year mission proper didn't begin until after the ship got back from the galaxy's edge and underwent a refit to its series configuration, since it makes no sense for such an extensive refit to happen during an ongoing mission. But I was instructed not to state that outright on the grounds that it might confuse casual readers, so I left it implicit.
I've mentioned this before in another thread that if one were to take Gene Roddenberry's novelization of 'The Motion Picture' at face value in the early chapters he lays out a timeline of Captain Kirk and the Enterprise prior to the events of the 'Motion Picture'.
Based on that information, the timeline could be laid out thusly
9 years ago - Kirk takes command of the Enterprise (Chapter 5)
8 years ago - Start of the FYM (Chapter 11)
7 years ago - Christine Chapel joins the Enterprise (Chapter 11)
3 years ago - End of the FYM. Kirk is promoted to Admiral. McCoy retires. Scotty begins redesigning and refitting the Enterprise (Chapters 7, 9)
2.8 years ago - Spock begins studying Kolinahr on Vulcan (Chapter 2)
2 1/2 years ago - Kirk is placed in charge of Starfleet Operations (Chapter 5)
2 years ago - Chapel earns her doctorate and becomes an M.D. (Chapter 11)
18 months ago - Kirk recommends Captain Decker oversee the Enterprise refit and command her once it is completed (Chapter 3)
As you can see, there is a one-year gap between the time that Kirk took command of the Enterprise and the start of the FYM. Plenty of space for 'WNMHGB' and other adventures before the Enterprise returns to Earth to be refitted from the Pilot version to the Series version.