Symmetric Matrices & Quadratic Forms · Superchallenge problem

Five real numbers $x_1, \ldots, x_5$ sit around a circle, with $x_1^2 + x_2^2 + x_3^2 + x_4^2 + x_5^2 = 1$. Find the maximum of $(x_1 - x_2)^2 + (x_2 - x_3)^2 + (x_3 - x_4)^2 + (x_4 - x_5)^2 + (x_5 - x_1)^2$.