$$4x^5+5x^3+x-1 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.4542 & x_2 = -0.34343+0.6082i & x_3 = -0.34343-0.6082i \\[1 em] x_4 = 0.11633+1.0558i & x_5 = 0.11633-1.0558i \\[1 em] \end{matrix} $$
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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