At the end of a professional bowling tournament, the top 5 bowlers have a playoff. First, bowler #5 competes against bowler #4. The loser receives the 5th prize, and the winner competes against bowler #3 in another game. The loser of this game receives the 4th prize, and the winner competes against bowler #2. The loser of this game receives the 3rd prize, and the winner competes against bowler #1. The winner of this game gets the 1st prize, and the loser gets the 2nd prize. In how many orders can bowlers #1 through #5 receive the prizes? Provide your answer as an integer.

Let's think step by step and output the final answer within \boxed{}.
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