it sounds like you have php version numbers confused with version numbers for some other application. You can find out what the latest versions are at php.net. Believe me, anyone who tells you some app requires PHP 6.5 is pulling your leg.
if yours is a dedicated server, you can probably install whatever you please, I would imagine (don't know from experience, being a downscale shared server kind of guy). But if you don't know, e.g., what SSH is, then compiling PHP 5 from source will probably be more of an adventure than you would enjoy. But if you want to have a wack at it, try it on a non-production machine first. I daresay there are plenty of folks here who have built PHP just a few times
and can help with your questions. And yes, make sure your PHP apps support PHP 5. A lot of PHP 5 code will not even parse on PHP 4 -- that is, PHP 5 has a wider vocabulary than PHP 4, stuff that PHP 4 does not understand.
if you really need PHP 5, perhaps your hosting company can set it up for you for a nominal fee (again, speculation on my part).