The mysql transition *shouldn't* be a problem for you. If you move to a host that uses MySQL 5.6 however, you may run into problems with having MySQL users that are using an old form of encryption.

As far as PHP goes we are successfully running Concrete5 under PHP 5.5.15 and no issues. The only slight concern might be any additional add-ons that you might be running not supporting these, but so far I haven't run across any issues.

We've migrated several sites up from PHP 5.3 to 5.5 and MySQL 5.1 to 5.5 with no issues. Moving up to MySQL 5.6 is where occasionally you need to reset your database user passwords, but is usually not a big deal.

Thank you so much for the response. I'm going to have the server imaged before I proceed. Hopefully everything will go smoothly.