If what they sold you is a 58 or 59 cm bike, then you're pretty much on the money. A larger frame would likely mean reaching too far forward for the handlebar, and smaller would mean reaching too low. One advantage to having long arms is being able to reach lower without upsetting things too much.

As a data point, I'm 182 or 183 cm tall, with 89.5 cm legs. I've been riding bikes this size since 1970. Eddy Merckx is 184 cm (or was before he got old), with long arms and legs. That's his size, too.