Upgrading a database server(and especially MySQL) requires more than a few simple launch-install steps. You have to make sure that the old database is compatible with the new structure and functions provided by the new version. There are also changes that have been implemented in new versions which might not be compatible with what you have. Kindly study the documentation page that I linked below to take all the necessary steps to prepare for a database update.
Note: As a friendly reminder, follow this saying "if it isn't broken, don't fix it". Of course there are security exceptions, but if the MySQL is working fine and all the updates are working fine as well, don't migrate to a much higher version unless you are told so.
I recommend checking the MySQl Upgrade documentation because the procedure is different for the available operating systems.
