Let the number be n. 

If the number is divided by 3 it leaves 5 as remainder. 

By Euclid’s division lemma, 

n = 3q + 5 where q is quotient 

3n = 3(3q+5) 

3n = 9q + 15 

3n + 3 = 9q + 18 

= 3 $\times$ 3q + 3 $\times$ 6 = 3 (3q + 6) 

Hence, the remainder is 0.