Might be time to consider installing VirtualBox on a laptop ... flavor or your choice (I happen to use a Mac laptop) ... install a guest OS - the same CentOS version and use that as your playground for learning what really is the best tool for Linux boxen ... the command line (my humble opinion of course! - but when it comes to updating/upgrading Moodle find the command line using git *is* the way to go.).
I've done that recently due to upgrade requirements for PHP and MySQL (CentOS doesn't have the versions required in their repo but they are available in 3rd party repos like the one Moodle recommends using webtatic.
And, the newer version of PHP does something different on CentOS 5 (probably 6 as well) in that mysqlnd is default rather than mysqli. Installing 2.7 has no option for mysqlnd ... only mysqli.
So one learns the work-arounds, etc. on something that could be blown away. One is then prepared for attacking the production Moodle server and there will be less likelihood of something major holding you up.
Still ... 2.7 *is* a .0. Might wait until it's a 2.7.2 before making that leap. It is supposed to be a long term support version so you do want to get there, but there is nothing pressing if you are running a 2.5 or 2.6 for a while.
Upgrades to PHP and MySQL affect any/all apps that use them ... have a wordpress on the same server? That could be affected by the upgrades to PHP and MySQL. So that is also true of a 2.4 site (another domain) or a 2.5, or a 2.6 ... they all use the same copy of PHP and the same MySQL (normally). Unless you really know what you are doing and have a big box that could handle running multiple versions of PHP and of MySQL. That, is guruish, BTW.
My 2 'sense' ... uhhh, nope, spelled it right! ;)
'spirit of sharing', Ken