\(x^5-x^3=0\)
\(=x^3\left(x^2-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x^3=0\\x^2-1=0\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x^3=0^3\\x^2=1\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x\in\left\{-1;1\right\}\end{matrix}\right.\)
