The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1+2i\\[1 em]x_2 &= -1-2i \end{aligned} $$The solutions of $ x^2+2x+5 = 0 $ are: $ x = -1+2i ~ \text{and} ~ x = -1-2i$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.