$$x^{10}-5x^9+x^8+26x^7-21x^6-49x^5+40x^4+42x^3-20x^2-15x-1 = 0$$
Answer
$$ \begin{matrix}x_1 = -0.07534 & x_2 = -0.46968 & x_3 = -1.25523 \\[1 em] x_4 = 1.07534 & x_5 = -0.90192 & x_6 = -1.48305 \\[1 em] x_7 = 1.46968 & x_8 = 1.90192 & x_9 = 2.25523 \\[1 em] x_10 = 2.48305 & \\[1 em] \end{matrix} $$
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