Answer
$x=\{ -5,0,5 \}$
Work Step by Step
The factored form of the given expression, $
5x^5=125x^3
,$ is
\begin{align*}
5x^5-125x^3&=0
\\
5x^3(x^2-25)&=0
&\text{ (factor $GCF=5x^3$)}
\\
5x^3(x+5)(x-5)&=0
&\text{ (use $a^2-b^2=(a+b)(a-b)$)}
.\end{align*}
Equating each factor to zero (Zero Product Property) results to
\begin{align*}
5x^3=0
\\\\\text{ OR }\\\\
x+5&=0
\\\\\text{ OR }\\\\
x-5&=0
.\end{align*}
Solving each of the equations above results to
\begin{align*}
5x^3&=0
\\
\dfrac{5x^3}{5}&=\dfrac{0}{5}
\\
x^3&=0
\\
x&=\sqrt[3]{0}
\\
x&=0
\\\\\text{ OR }\\\\
x+5&=0
\\
x+5-5&=0-5
\\
x&=-5
\\\\\text{ OR }\\\\
x-5&=0
\\
x-5+5&=0+5
\\
x&=5
.\end{align*}
Hence, the real solutions are $
x=\{ -5,0,5 \}
$.
