Do Army E5s live in the barracks on Eglin AFB?

I assume you're PCSing to 7th SFG, since there are no 35F slots at Ranger School, in which case the SF compound has barracks for you.

long time ago but when I was an E5 on Eglin you either lived in the barracks or you had the option to live off base at your own expense. You did not get BAH because you had a room in the barracks (which you had to maintain by the way). But that was in the late 80s.

depends on barracks availability. General rule is single , unaccompanied Soldiers in the rank of Sergeant or below, will live in the barracks. the exception is a certificate of unavailability, which is provided by the appropriate barracks manager facility.