How long should a golf driver shaft be if you are 5'6'' tall?

There's not enough information given hereto know. Golf clubs should be fit to the height of your hand not your head. There are a few theories that go around, but all are based on measuring something about your hand. Most go by the height that the tip of your middle finger is above the ground, but some say the seam between your wrist and hand. Measure that and find out where it fits on a chart of club lengths. Probably you would be best fit with something a bit shorter than the standard 43" driver, but it's hard to say. Dave Tutelman's design notes are an Excellent resource for figuring out such things.