Is there a way to change my "most recent 5k time"?

That’s an interesting request. Did you enter it wrong? The moment you run a better time in your next training, it should adjust your subsequent sessions. The initial time is to provide guidance for the algorithm.

I put what it would have been based on a recent 10k. However, I'm planning to run another 5k next week so will likely have a more accurate time. My actual marathon race training doesn't start til July.
I haven't dug too deeply into the app...will it record a run that's not part of the training plan?

Yes. Just go to the tracking section. And track your 5k, via the gps of your phone. It will use that data to adjust your future trainings