Hi, Chris,
Check the amount of free space on your drive. Make sure that you have enough to handle your movie. Probably need 30-40GB.
Since the thumbnails disappear while editing, it might be that your computer processor is not powerful enough to handle the editing in real time with 5000 photos in the project. Possibly this is the issue if you have an i5 processor versus the more powerful i7. Check your computer specs to see. Also, you want at least 4GB of RAM.
What you might do is to split your project into 3 or 4 projects, i.e, into more manageable segments. Then edit them separately and combine them into one project at the end.
To make sure that the issue is confined to this project, and not global, it would be helpful to test a couple of other projects to see if the issue happens there.
Another thing you can try is to boot up in Safe Mode (see Finder help menu for instructions) and, after everything loads, immediately shut down and reboot in normal mode. See if that helps.
-- Rich