$$-x^5+7x^4+59x^3-320x^2+268x+504 = 0$$
Answer
$$ \begin{matrix}x_1 = -0.86389 & x_2 = -7.37658 & x_3 = 10.01751 \\[1 em] x_4 = 2.61148+1.03694i & x_5 = 2.61148-1.03694i \\[1 em] \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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