$$19x^5+10x^4-50x^3-50x^2+20x+60 = 0$$
Answer
$$ \begin{matrix}x_1 = 1.10242 & x_2 = -1.45487 & x_3 = 1.47296 \\[1 em] x_4 = -0.82341+0.81161i & x_5 = -0.82341-0.81161i \\[1 em] \end{matrix} $$
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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