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