The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.3778\\[1 em]x_2 &= -3.3402\\[1 em]x_3 &= 3.9624 \end{aligned} $$Polynomial $ x^3-x^2-13x+5 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.