Hmm, interesting that it happened randomly one day (and presumably stayed that way ever since). It could be that another program/service was installed that day, and it also uses Qt5 DLLs (see the DLL issues in this thread).
Maybe try GPlates 2.5. I made a change to try to avoid GPlates using a Qt5 DLL that’s already loaded in memory (by another program/service). Not sure if it works though (see here), but worth a try.