Explanation

There are 9000 four-digit numbers (1000–9999). Numbers with no digit 5: the thousands digit has 8 choices (1–9 except 5) and each of the other three digits has 9 choices (0–9 except 5), giving 8 × 9³ = 5832. Subtracting from 9000 gives 9000 − 5832 = 3168 numbers containing at least one 5.