If $x_1$, $x_2$, ..., $x_6$ $\in $ $[0,1]$, prove that the cyclic sum of $\frac{x_1^3}{x_2^5+x_3^5+x_4^5+x_5^5+x_6^5+5}$ is less than $\frac{3}{5}$.
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Tags: inequalities unsolved, inequalities
If $x_1$, $x_2$, ..., $x_6$ $\in $ $[0,1]$, prove that the cyclic sum of $\frac{x_1^3}{x_2^5+x_3^5+x_4^5+x_5^5+x_6^5+5}$ is less than $\frac{3}{5}$.