$$126392x^5+412708x^4+531578x^3+336367x^2+104000x+12463 = 0$$
Answer
$$ \begin{matrix}x_1 = -0.35233 & x_2 = -0.67394 & x_3 = -0.71324 \\[1 em] x_4 = -0.7629+0.01493i & x_5 = -0.7629-0.01493i \\[1 em] \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
This page was created using
Polynomial Equations Solver