Usually it's just a case of running the new setup program and overwriting the existing version of AwareIM, specifying MySQL as the database and at the end of the process, just tell the installer to use your existing MySQL settings.
I normally back up both the database AND the working AwareIM directory before starting - and of course it goes without saying you need to stop AwareIM before doing the upgrade.
There may be issues if you are several versions behind (like going from V3 to V5 ) You'd need to email support for a definitive answer on that, but 4.9 to 5 is a walk in the park