If a number is divisible by 5 and 6 both, then it may not be divisible by

1. 10

2. 15

3. 30

4. 60

5 and 6 are co-prime, so any number divisible by both is divisible by 5 × 6 = 30.

So the number is divisible by every factor of 30, namely 1, 2, 3, 5, 6, 10, 15 and 30.

But 60 is not a factor of 30, so the number may not be divisible by 60. (For example, 30 itself is divisible by 5 and 6 but not by 60.)

Hence, option 4 is the correct option.