The Collaborative International Dictionary of English v.0.48:

High five \High five\
   1. See Cinch (the game).
      [Webster 1913 Suppl.]

   2. pl. a celebratory or mutually congratulatory gesture
      between two persons performed by each slapping the other's
      raised right hand. Also used as a verb.
      [PJC]

The Collaborative International Dictionary of English v.0.48:

Cinch \Cinch\, n. [Cf. cinch a girth, a tight grip, as v., to
   get a sure hold upon; perh. so named from the tactics used in
   the game; also cf. Sp. cinco five (the five spots of the
   color of the trump being important cards).]
   A variety of auction pitch in which a draw to improve the
   hand is added, and the five of trumps (called right pedro)
   and the five of the same color (called left pedro, and
   ranking between the five and the four of trumps) each count
   five on the score. Fifty-one points make a game. Called also
   double pedro and high five.
   [Webster 1913 Suppl.]