$0={x}^{5}-5{x}^{3}$
Swap the sides of the equation${x}^{5}-5{x}^{3}=0$
Factor out ${x}^{3}$ from the expression${x}^{3} \times \left( {x}^{2}-5 \right)=0$
When the product of factors equals $0$, at least one factor is $0$$\begin{array} { l }{x}^{3}=0,\\{x}^{2}-5=0\end{array}$
Solve the equation for $x$$\begin{array} { l }x=0,\\{x}^{2}-5=0\end{array}$
Solve the equation for $x$$\begin{array} { l }x=0,\\x=-\sqrt{ 5 },\\x=\sqrt{ 5 }\end{array}$
The equation has $3$ solutions$\begin{align*}&\begin{array} { l }x_1=-\sqrt{ 5 },& x_2=0,& x_3=\sqrt{ 5 }\end{array} \\&\begin{array} { l }x_1\approx-2.23607,& x_2=0,& x_3\approx2.23607\end{array}\end{align*}$