$$-x^5+31x^4+149x^3+985x^2-2655x+2480 = 0$$
Answer
$$ \begin{matrix}x_1 = 35.86429 & x_2 = 1.0857+0.77221i & x_3 = 1.0857-0.77221i \\[1 em] x_4 = -3.51784+5.1557i & x_5 = -3.51784-5.1557i \\[1 em] \end{matrix} $$
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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Polynomial Equations Solver