\(\frac{5-n}{2n+1}\) nguyên \(\Rightarrow\frac{-2\left(5-n\right)}{2n+1}\) nguyên \(\Rightarrow\frac{2n-10}{2n+1}\) nguyên
\(\Rightarrow\frac{2n+1-11}{2n+1}\) nguyên \(\Rightarrow1-\frac{11}{2n+1}\) nguyên \(\Rightarrow\frac{11}{2n+1}\) nguyên
\(\Rightarrow2n+1=Ư\left(11\right)=\left\{-11;-1;1;11\right\}\)
\(2n+1=-11\Rightarrow n=-6\)
\(2n+1=-1\Rightarrow n=-1\)
\(2n+1=1\Rightarrow n=0\)
\(2n+1=11\Rightarrow n=5\)
Thử lại thấy cả 4 giá trị đều đúng, vậy \(n=\left\{-6;-1;0;5\right\}\)