Show that for every integer $n \geq 2$ the number $$a=n^{5n-1}+n^{5n-2}+n^{5n-3}+n+1$$is a composite number.
Source: Moldova TST 2022
Tags: number theory
Show that for every integer $n \geq 2$ the number $$a=n^{5n-1}+n^{5n-2}+n^{5n-3}+n+1$$is a composite number.