KöMaL 2013 B4585

Prove that if $x_1 \ge x_2 \ge x_3 \ge x_4 \ge x_5 \ge$0, then ${(x_1+x_2+x_3+x_4+x_5)}^2\ge \frac{25}{2} \big(x_4^2+x_5^2\big)$. What is the condition for equality?