The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.5641\\[1 em]x_2 &= 0.2821+2.2888i\\[1 em]x_3 &= 0.2821-2.2888i \end{aligned} $$Polynomial $ x^3+5x+3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.