\(2^{\left(x-5\right)\left(x+2\right)}=1\)
\(\Rightarrow2^{\left(x-5\right)\left(x+2\right)}=2^0\)
\(\Rightarrow\left(x-5\right)\left(x+2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-5=0\\x+2=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=5\\x=-2\end{matrix}\right.\)
Vậy \(x\in\left\{5;-2\right\}\)