$$-x^5+19x^4+190x^3+260x^2-2942x+2260 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.8864 & x_2 = 2.44881 & x_3 = 26.41152 \\[1 em] x_4 = -5.37336+3.24781i & x_5 = -5.37336-3.24781i \\[1 em] \end{matrix} $$
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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