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Originally Posted by Jake
I need to check whether Joomla would run with mySQL 5.7.
Yes, Joomla will also work with newer versions of MySQL. However, I would upgrade to MariaDB (https://en.wikipedia.org/wiki/MariaDB) instead.

Originally Posted by Jake
If there anything special that needs to be done prior to upgrading mySQL? Other than a full backup?
No, just create a full backup of your databases