Dominion Tower V is a music track that is unlocked when reaching tier 3 of the Dominion Tower in any mode at the Dominion Tower (Climber, Endurance, Special, Freestyle, or Spectator).
A recommended way to go about unlocking the tracks is to do the Sunfreet special challenge. You can turn your playlist between on and off constantly to change which track occurs. For example, if you have Dominion Tower I and IV unlocked, and you go to the Sunfreet challenge floor, Dominion Tower IV may play again. Turning your playlist on and then off will reset which song plays. So it may be Dominion Tower I, II, III, IV, or V. This means players do not have to keep entering and exiting floors.
This track along with Dominion Tower I, Dominion Tower II, Dominion Tower III, and Dominion Tower IV aren't unlocked in a specific order. All 5 can be unlocked by simply entering any mode, leaving and repeating the process. This may take several tries due to the random ordering giving you the same track more than once upon re-entering. The tracks may also be unlocked by spectating fights, which can be done at any combat level.