The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.8662\\[1 em]x_2 &= 2.2108\\[1 em]x_3 &= 3.6554 \end{aligned} $$Polynomial $ x^3-5x^2+3x+7 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.