OBM 2005 Problem 2

Determine the smallest real number $C$ such that the inequality $$C(x_1^{2005} +x_2^{2005} + \cdots + x_5^{2005}) \geq x_1x_2x_3x_4x_5(x_1^{125} + x_2^{125}+ \cdots + x_5^{125})^{16}$$ holds for all positive real numbers $x_1,x_2,x_3,x_4,x_5$ .