Hi,
A5000 BTU room AC only draws about 5 amps when running.
https://www.frigidaire.com/Home-Comfort/Air-Conditioning/Window-Mounted-AC/FFRA0511R1/
So, an extension cord rated at 15 or 20 amps should be fine.
The GFCI does not provide any overcurrent (short circuit) protection -- it just protects people against a ground fault in system. It measures ingoing and outgoing current and shuts the circuit down if the ingoing exceeds the outgoing by more than a few milliamps -- the idea being that a person touching something that is hot because of a ground fault is conducting the missing current to ground and being electrocuted. So, its good to have, but it does not protect against the case where there is a short of the hot wire to ground which might draw enough current to overheat the extension cord and cause a fire.
The RV park or campground 30 amp power pedestal is likely fused to 30 amps, so a short circuit that draws more than 30 would trip that fuse or breaker.
Most of the power pedestals that have a 30 amp outlet also have a 15 amp 120 VAC outlet, so you could just plug into that one.
It should be plenty to power a 5500 BTU AC.
Gary