Can you reset private mode on a Samsung Galaxy S5? I set up private mode when I first got the phone, but now I can't seem to remember the password; it's none of my usual ones. Is it possible to reset (read: wipe) private mode and start over, without having to factory reset the whole phone? 

I have root, if that helps.
Did you try to install Samsung Kies on your PC? Try to download it, connect your device and click the Backup/reset tab, and then click "Data backup".

The easiest way it factory reset. If you have any private data who you don't want to loose say what sort is it, there are numerous ways to backup them.