Solution:

The given 5 digits (1, 2, 5, 7 and 8) should be arranged among themselves in order to get all possible 5-digit numbers.

The number of ways for doing this can be done using the factorial.

5! = 5 × 4 × 3 × 2 × 1 = 120

Answer: Therefore, the required number of 5-digit numbers is 120.