Copy mysql schemas to a new instance of a new version
You should be able to just mysqldump the individual databases and load them straight into a MySQL instance running on the latest version. I have recommended this before:


May 26, 2015 : mysql upgrading from 5.1 --&gt; 5.6 do I have to do mysqldump before upgrade?
Oct 17, 2014 : Any known issues upgrading from MySQL 5.1.73 to 5.6.21?
Apr 18, 2013 : Steps to upgrade MySQL from version 5.0 to version 5.5
Apr 11, 2013 : MySQL upgrade 5.0.88 to latest


When doing this, please do not move the grants by dumping the mysql schema. The number of columns have changes between versions : 


Oct 10, 2014 : MySQL service stops after trying to grant privileges to a user
Jun 13, 2012 : Fastest way to move a database from one server to another


Try to extracts the grants with pt-show-grants or emulate it as suggested