For any positive integer n, n^3 + 5n is divisible by 6. This is because 6 divides 6n for all integers n. Additionally, (n^3-n) can be factored into (n-1)n(n+1), where one term is divisible by 3 and one by 2, so their product is divisible by 6. Since 6 divides both 6n and (n^3-n), it must divide their sum, n^3 + 5n.