$$871x^4+629x^3+791x^2+438x+5 = 0$$
Answer
$$ \begin{matrix}x_1 = -0.01166 & x_2 = -0.59307 & x_3 = -0.05872+0.90927i \\[1 em] x_4 = -0.05872-0.90927i & \\[1 em] \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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Polynomial Equations Solver