Question 1021206
By Fermat's little theorem, *[tex \large n^5 \equiv n \pmod{5}]. So *[tex \large n^5 - n \equiv n - n \equiv 0 \pmod{5}].


You can also verify by checking n = 0, 1, 2, 3, 4. This is sufficient to prove that the statement holds for all natural n.