\(\left(n+2\right)⋮\left(n-3\right)\)
\(\Rightarrow\left(n-3\right)+5⋮\left(n-3\right)\)
Mà \(\left(n-3\right)⋮\left(n-3\right)\Rightarrow5⋮\left(n-3\right)\)
\(\Rightarrow n-3\inƯ\left(5\right)=\left\{1;-1;5;-5\right\}\)
\(\Rightarrow n\in\left\{4;2;8;-2\right\}\)
Vậy n \(\in\left\{4;2;8;-2\right\}\)