Klitschko, taller with a longer reach, controlled the fight at will, scoring with left jabs and straight rights with hardly any opposition from the Australian challenger.
Leapai went down when he was hit with a left-right combination. He got up but Klitschko put him away for good with 58 seconds left in the fifth.
Klitschko recorded his 53rd KO in 62 wins, with three defeats. Leapai dropped to 30-5, with three draws.