A plays B.  call the winner A by symmetry.
A plays C 
IF A WINS, D plays E, and winner plays A best-of-3
IF C WINS, A plays C again
   IF A WINS, C plays D
      IF C WINS, A plays E and winner plays C
      IF D WINS, D plays E and winner plays A
   IF C WINS, C plays D
      IF C WINS, C plays E twice (C wins ties)
      IF D WINS, C plays E and winner plays D