The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.2951\\[1 em]x_2 &= -0.6346\\[1 em]x_3 &= 5.3395 \end{aligned} $$Polynomial $ x^3-5x^2-2x+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.