The probability of Xiao Ming winning the prize is 13/25. Because any one of 1 ~ 5 may appear in the first round and any one of 1 ~ 5 may appear in the second round, there are 5x5 = 25 * * *, of which only 13 appears even in the second round.

They are (1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (3, 1), (3,