Learn to dance and have FUN!
So at a social dance you end up getting paired with a 5' 9" girl for 1 dance, go with the flow. So you wont be able to dance smooth or American tango in closed position, who cares? Dance socially (where there is no body contact between the 2 of you) and navigate her at angles around the floor so you can see whos behind her to protect her back. Remember, its only a 2 or 3 min song.
Im 6' 1" in heels. Ive danced with much shorter guys MANY, MANY times. The only thing that WILL bug a girl is when you dont get your arm up high enough to clear her head on turns. If the height difference is really all that great, nothing wrong with doing free spins.
There is a way to work every situation. Height should NOT be a deterrent to learning to dance.