The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 3.5755\\[1 em]x_2 &= -0.1877+1.1433i\\[1 em]x_3 &= -0.1877-1.1433i \end{aligned} $$Polynomial $ 5x^3-16x^2-24 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.