The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.9426\\[1 em]x_2 &= -0.7034+0.7674i\\[1 em]x_3 &= -0.7034-0.7674i\\[1 em]x_4 &= 0.2322+1.3798i\\[1 em]x_5 &= 0.2322-1.3798i \end{aligned} $$Polynomial $ -2x^5-3x^3+4 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.