To upgrade MySQL select the MySQL version you want to install from WHM > Tweak Settings.
Then login via shell and run below command :
/scripts/mysqlup --force
Once the installation is complete , check MySQL version and then compile php/apache so that it can load new libraries by using below command :
/scripts/easyapache
You may select modules and other settings according to your choice from easyapache menu.
Once its complete you are done !