HALMA is a 5 letter word that starts with H.

1. \Hal"ma\, n. [NL., fr. Gr. ?, fr. ? to leap.] (Greek
   Antiq.)
   The long jump, with weights in the hands, -- the most
   important of the exercises of the Pentathlon.
   
   

2. \Hal"ma\, n.
   A game played on a board having 256 squares, by two persons
   with 19 men each, or by four with 13 men each, starting from
   different corners and striving to place each his own set of
   men in a corresponding position in the opposite corner by
   moving them or by jumping them over those met in progress.