[tex]\it \left.\begin{aligned}{x\in\mathbb{Z}\\ \\ \dfrac{-5}{x+1}\in \mathbb{Z}\end{aligned}\right\} \Rightarrow x+1\in D_5 \Rightarrow x+1\in\{\pm1,\ \pm5\} \Rightarrow x+1\in\{-5,\ -1,\ 1,\ 5\}|_{-1}\Rightarrow\\ \\ \\ \Rightarrow\ x\in\{-6,\ -2,\ 0,\ 4\}[/tex]
