Which Horse Breeds Are Five Gaited?

What horse breeds are five gaited?

A "Gaited" horse is one which performs any of the four-beat natural gaits in place of or in addition to the trot. These gaits are the stepping pace, the rack, the running walk, saddle, single-foot, and the fox-trot. Three-gaited refers to horses that are trained in the walk, trot, and canter; and five-gaited horses are those trained in all five. As far as I am aware, the only horse breed which is often five-gaited is the American Saddlebred Horse.