On my desktop, I first tried deleting all of the favorites and then creating my own. When I tried to save the new favorite, the program hung. Comparing to what's on my laptop, I saw that the F5\settings\favorites\list.ini file had disappeared. So I created an empty file of that name and I was later able to save a favorite. That resulted in two files in that folder:
On my laptop, I can create a new map with two layers, and it later displays correctly every time.
Complicating this, every time I select "Add/Edit Favorites" from the menu, the favorites dialog opens but immediately tucks itself behind the main F5 window. Somehow, Windows still thinks it's the window that's currently on top -- because, when I use the Alt-Tab key combination, Windows brings up a collection of window thumbnails and moves the selected one to F5. To get to the favorites window, I have to Alt-Tab many times or right-click the F5 icon on my Windows 10 taskbar. I'm a keyaboard oriented person, so mousing is not my first thought. If you can, please persuade the favorites window to remain on top after it opens.
But that's not my primary problem. On the desktop, I simply cannot display the favorite that I have stored.
Offer: If it will help you to diagnose this, which is probably a pretty obscure bug, I could grab off a snapshot copy of all of the files in my installation of F5, then uninstall and reinstall the program. Comparison of the newly installed files to the saved files might give a clue. Let me know if you'd like me to try this.