\(\Delta=\left(2m-1\right)^2-4\left(m^2-m\right)=1>0\)
Phương trình luôn có 2 nghiệm: \(\left\{{}\begin{matrix}x_1=\frac{2m-1-1}{2}=m-1\\x_2=\frac{2m-1+1}{2}=m\end{matrix}\right.\)
\(x_1^2+mx_2-5=0\)
\(\Leftrightarrow\left(m-1\right)^2+m^2-5=0\)
\(\Leftrightarrow2m^2-2m-4=0\Rightarrow\left[{}\begin{matrix}m=-1\\m=2\end{matrix}\right.\)