did you tested mysql driver in Qt5 with mingw?
i've created libmysql.a just like i was before with Qt4. when i try to load the driver, fails but afterward lists QMySQL and QMySQL3 as available drivers.
Same bug occurred to me some times ago with msvc not mingw and in windows. after a while i've found that i have to add mysql drivers to envirenment path!!
doesn't affect. the problem seems to be a kind of incompatibility with some prototypes or something in lib symbols. other drivers on same path loaded with no problem.