$$7x^5-33x^4-4x^2+3x+52 = 0$$
Answer
$$ \begin{matrix}x_1 = -1.02696 & x_2 = 1.19272 & x_3 = 4.7209 \\[1 em] x_4 = -0.08619+1.13015i & x_5 = -0.08619-1.13015i \\[1 em] \end{matrix} $$
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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