$$784h^5+5933h^4-13405 = 0$$
Answer
$$ \begin{matrix}h_1 = 1.18232 & h_2 = -1.28438 & h_3 = -7.56237 \\[1 em] h_4 = 0.04841+1.21924i & h_5 = 0.04841-1.21924i \\[1 em] \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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