Gọi $\overrightarrow{c}=m\overrightarrow{a+n\overrightarrow{b}, (m,n\in R)$
=> $\overrightarrow{c}=(2m+n;-2m+4n)$
Theo bài ra : $\overrightarrow{c}=(5; 0)$
<=> $\left\{\begin{matrix}2m+n=5 & \\ -2m+4n=0 & \end{matrix}\right.$
<=> $\left\{\begin{matrix}m=2 & \\ n=1 & \end{matrix}\right.$
=> $\overrightarrow{c}=2\overrightarrow{a}+\overrightarrow{b}$