The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.3003\\[1 em]x_2 &= 0.6728+1.1067i\\[1 em]x_3 &= 0.6728-1.1067i\\[1 em]x_4 &= -0.5729+1.1298i\\[1 em]x_5 &= -0.5729-1.1298i \end{aligned} $$Polynomial $ 2x^5-3x^4+4x^3-5x^2+6x-7 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.