**Solution:**

By Euclid’s division lemma, we have

a = bq + r; 0 ≤ r < b

For a = n and b = 5, we have

n = 5q + r …(i)

Where q is an integer

and 0 ≤ r < 5, i.e. r = 0, 1, 2, 3, 4.

Putting r = 0 in (i), we get

n = 5q

=> n is divisible by 5.

n + 4 = 5q + 4

=> n + 4 is not divisible by 5.

n + 8 = 5q + 8

=> n + 8 is not divisible by 5.

n + 12 = 5q + 12

=> n + 12 is not divisible by 5.

n + 16 = 5q + 16

=> n + 16 is not divisible by 5.

Putting r = 1 in (i), we get

n = 5q + 1

=> n is not divisible by 5.

n + 4 = 5q + 5 = 5(q + 1)

=> n + 4 is divisible by 5.

n + 8 = 5q + 9

=> n + 8 is not divisible by 5.

n + 12 = 5q + 13

=> n + 12 is not divisible by 5.

n + 16 = 5q + 17

=> n + 16 is not divisible by 5.

Putting r = 2 in (i), we get

n = 5q + 2

=> n is not divisible by 5.

n + 4 = 5q + 9

=> n + 4 is not divisible by 5.

n + 8 = 5q + 10 = 5(q + 2)

=> n + 8 is divisible by 5.

n + 12 = 5q + 14

=> n + 12 is not divisible by 5.

n + 16 = 5q + 18

=> n + 16 is not divisible by 5.

Putting r = 3 in (i), we get

n = 5q + 3

=> n is not divisible by 5.

n + 4 = 5q + 7

=> n + 4 is not divisible by 5.

n + 8 = 5q + 11

=> n + 8 is not divisible by 5.

n + 12 = 5q + 15 = 5(q + 3)

=> n + 12 is divisible by 5.

n + 16 = 5q + 19

=> n + 16 is not divisible by 5.

Putting r = 4 in (i), we get

n = 5q + 4

=> n is not divisible by 5.

n + 4 = 5q + 8

=> n + 4 is not divisible by 5.

n + 8 = 5q + 12

=> n + 8 is not divisible by 5.

n + 12 = 5q + 16

=> n + 12 is not divisible by 5.

n + 16 = 5q + 20 = 5(q + 4)

=> n + 16 is divisible by 5.

**Thus for each value of r such that 0 ≤ r < 5 only one out of n, n + 4, n + 8, n + 12 and n + 16 is divisible by 5.**