Basically you'll have to be able to close overhead lockers, and, more importantly, be able to reach safety equipment stowed in overhead lockers.
I'm sure you'll be fine being 5'3. Put that on your application forms, and give it a shot. As Sylvestria said, most airlines won't actually measure you, and I never had to do a 'reach-test' either (saying that, I'm 5'10, so I guess there was no need.).
You have nothing to loose :-)