$$-7+u^5+4u = 0$$
Answer
$$ \begin{matrix}u_1 = 1.17943 & u_2 = 0.68886+1.28958i & u_3 = 0.68886-1.28958i \\[1 em] u_4 = -1.27858+1.06856i & u_5 = -1.27858-1.06856i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} -7+u^5+4u &= 0&& \text{simplify left side} \\[1 em]u^5+4u-7 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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