The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.1542\\[1 em]x_2 &= -0.5771+1.9998i\\[1 em]x_3 &= -0.5771-1.9998i \end{aligned} $$Polynomial $ x^3+3x-5 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.