Oh dear, that was unlucky. I've never previously seen that happen, but it's easy to prove that it can occur.
I'll log this issue on Audacity's issue tracker.
Super. That's a good original file. then right as it appears to finish it pops up and says RegSetEx failed. Error Code 5. Is that the full and complete message "RegSetEx failed. Error Code 5"? Is your computer behaving normally other than that? What security products do you have installed?
Is there any easy way to recover this? Probably not. If it was a fresh, unedited recording, then there's a slim chance of recovery (but not easy). If the project has been "worked on" (editing / processing), then no chance. Unfortunately it sounds like you are on the "no chance" ...
Thanks for this! But I do not get the box popping up when I open Audacity that asks for permission to use the microphone, and when I go to System Preferences, Audacity doesn't show up in the list!