$$x^5-15x^4+2150 = 0$$
Answer
$$ \begin{matrix}x_1 = 3.71524 & x_2 = -3.29261 & x_3 = 14.95704 \\[1 em] x_4 = -0.18983+3.42268i & x_5 = -0.18983-3.42268i \\[1 em] \end{matrix} $$
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