I use the latest 64 bit Linux version of the program on my desktop, but I have an old 32 bit netbook running the last 32 bit version of Linux Mint (19.3 Xfce).
I want to be able to load my working KMyMoney file onto the netbook when traveling, update it and reload it onto the desktop when I return.

The newest 32 bit version of KMyMoney that I could install on the netbook is 5.0.3
Is there a newer version of the program that will run on Linux 19.3 32 bit? If there is, where can I download it? I tried installing 5.0.8 but get unsatisfied dependencies failures.
Is there a newer 32 bit appimage I could get for that computer? If so, where is it available?

If there is no appimage, will I run into any issues updating the file, created with the newest version of the program, on 5.0.3 and then reusing the file later with the newest version of the program?

There are reasons why I need to take this particular netbook during certain travels rather than my newer 64 bit laptop.

Newer versions of KMyMoney depend on newer versions of Qt, KDE and other libraries. All of them have to be available on your netbook in 32-bit mode, so it is not only the application itself but a lot more. Regarding the exchange of the data files between the old and newer versions of KMyMoney I can't provide a definitive answer at this point. it mostly depends on the features you are using. A simple test would be to take a copy of your file, move it over to your netbook make some changes and move the file back to your newer system and see if everything still works (e.g. reports show the same numbers and content, data that you entered on the new system before is still present, etc.). Scanning through the logs of the XML plugin does not show any significant changes since 5.0.3 which would affect your endeavor, but that is no guarantee. Keep backups of your data files! Hope that helps.