China Western Mathematical Olympiad

Let $x_1,x_2,\dots ,x_5$ be nonnegative real numbers with ${\sum }_{i=1}^5\frac{1}{1+x_i}=1$. Prove that ${\sum }_{i=1}^5\frac{x_i}{4+x_i^2}\le 1$. (posed by Li Shenghong)