$$16x^5-20x^3+5 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.92417 & x_2 = 0.80051 & x_3 = -1.19679 \\[1 em] x_4 = -0.26395+0.53224i & x_5 = -0.26395-0.53224i \\[1 em] \end{matrix} $$
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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