The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.2016\\[1 em]x_2 &= 2.1284\\[1 em]x_3 &= -2.3301 \end{aligned} $$Polynomial $ x^3-5x+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.