I would do the upgrade on your test server first, to ensure everything goes as planned, and still functions properly. By "test server" I'm referring to an environment that is an EXACT duplicate of your Live environment from the OS, down to the versions of the packages on it.
If step one goes well, then:
Backup the data from the live environment.
Do the upgrade of the mysql and php on the live environment.
dance a jig for successful completion of upgrade.. (just don't let anyone see you... )