These dangerous beasts live on one unplottable island in northern Scotland. They have thick reddish fur and five legs.
Legend has it that two wizarding families lived on the island at one time—the McCliverts and the MacBoons.
One night, a gang of McCliverts transfigured the MacBoons into the hairy five-legged creatures. They realized too late that the MacBoons were way more dangerous in beast form than human form.
The McCliverts offered to turn them back into humans, but the MacBoons weren't having it. They killed all the humans on the island, which meant, of course, that there was no one with a wand to transfigure them back.
Of course, that story might not be true, and the Quintapeds seem perfectly happy to stay as they are, so that's how they remain. Guess being a beast isn't so bad.