I'm 5'6" too. The box for the Reebok ball says that 65cm is right for my height. The Reebok 65cm is a medium, which Reebok recommends for people who are 5'6"-5'11".
I've read varying recommendations online, though. (Before I bought the ball, I expected, based on what I'd read online, to get a 55cm ball. I trusted Reebok and went with their 65cm one.)
I bought a ball mainly to stretch out across--to get a long stretch across my back (laying on the ball, face up). I did that on a bigger ball (>65cm) and it was the right size for the stretch that I wanted. I didn't intend to do core work on the ball that I bought--just that stretching. However, on the ball that I bought, I don't get quite as much of a stretch as I do on the bigger ball, but it'll do.
Since I don't stretch on it the way I wanted to, I've found myself doing more core exercises on the ball and the 65cm size is perfect--any bigger and I wouldn't be able to balance safely.
Storing the ball is a challenge. The ball and the noise the sand inside makes weirds out my cat.