AT-OEMO-REG 2017 Problem 1

Let $x_1, x_2, \dots, x_n$ be non-negative real numbers such that $$x_1^2+x_2^2 + \dots x_9^2 \ge 25.$$ Prove that one can choose three of these numbers such that their sum is at least $5$.

Proposed by Karl Czakler