IMO 1971 — Shortlisted problems Question 5

(HUN 1) (IMO 1) Let $a,b,c,d,e$ be real numbers. Prove that the expression
$$(a-b)(a-c)(a-d)(a-e)+(b-a)(b-c)(b-d)(b-e)+(c-a)(c-b)(c-d)(c-e)$$
$$+(d-a)(d-b)(d-c)(d-e)+(e-a)(e-b)(e-c)(e-d)$$
is nonnegative.