None of those version are compatible with php 5.5. You'd need to upgrade to 4.2.3+ and 3.8.9+ respectively to be compatible with your new php version. The MySQL version should be fine for all three.
If they are going to migrate you to a new server you may want to ask them to install MariaDB instead of MySQL as the database. MariaDB is a drop in replacement (i.e. no changes need to be made to any software interacting with the database) and has a bunch of improvements.
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