The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.6319\\[1 em]x_2 &= -1.4252\\[1 em]x_3 &= 1.0286+1.5077i\\[1 em]x_4 &= 1.0286-1.5077i \end{aligned} $$Polynomial $ x^4+5x+3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.