Prove that n(n+5) + 2(n+3) is always a product of two numbers with a difference of 5.

n(n+5)+2(n+3) = n²+5n+2n+6 = n²+7n +6 = (n+6)(n+1) = (n+6) x (n+1).
The difference between (n+6) and (n+1) is 5, so this is a product of two numbers with a difference of 5.