Question
$$4x^5(x+5)^3 = 5$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 4x^5(x+5)^3 &= 5&& \text{simplify left side} \\[1 em]4x^5(x^3+15x^2+75x+125) &= 5&& \\[1 em]4x^8+60x^7+300x^6+500x^5 &= 5&& \text{move all terms to the left hand side } \\[1 em]4x^8+60x^7+300x^6+500x^5-5 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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