The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.5758\\[1 em]x_2 &= 1.1873\\[1 em]x_3 &= 4.3885 \end{aligned} $$Polynomial $ x^3-5x^2+2x+3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.