We have Moodle 2.7.2+ and the server we are on is running PHP version native (5.4) but I have the option to opt for 5.5
I see that there is 2.7.5+ and 2.8.3+ available, and the 2.8.3+ needs PHP 5.4.4
Should I leave it as it is, or go for an upgrade, in which case am I OK with the current native (5.4) PHP or should I move to 5.5?
You should never get yourself in a position where upgrading is a major hassle. That's how you end up using a several year old, unsupported release and - while I don't want to overstate the case - that should not be seen as good practice on the security and stability front.
I recommend making regular, small upgrades. You get used to doing it and any issues that do crop up are likely to be minor and easy to fix.