$$(2p-2)(p^4-3p^2+4) = 0$$
Answer
$$ \begin{matrix}p_1 = 1 & p_2 = 1.32288+0.5i & p_3 = 1.32288-0.5i \\[1 em] p_4 = -1.32288+0.5i & p_5 = -1.32288-0.5i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (2p-2)(p^4-3p^2+4) &= 0&& \text{simplify left side} \\[1 em]2p^5-6p^3+8p-2p^4+6p^2-8 &= 0&& \\[1 em]2p^5-2p^4-6p^3+6p^2+8p-8 &= 0&& \\[1 em] \end{aligned} $$
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