If the ship suffered damage during the shakedown mission, that would be plausible. But it seems the ship just sprouted a hundred design flaws unrelated to any shaking down. If turbolift doors don't work or the Captain's Log dictating machine breaks down, that's not combat damage the ship is recovering from, nor is it something Kirk would have tolerated for five or ten months before telling Scotty to get it fixed.
although the stardates between Star Trek IV and Star Trek V do tend to suggest several months elapsed between them
Fair enough. But we never learn any stardates for the latter part of ST4, after the actual action has wound down. That
was probably several months after the known stardates of ST4, and only a week or two before ST5.