[tex]\displaystyle\\
\frac{5}{2x-1} \in Z\\\\
\Longrightarrow (2x-1) \in D_{5Z}\\\\
D_{5z}=\{-5;~-1;~1;~5\}\\\\
2x - 1 = -5 \Longrightarrow 2x = -5+1\Longrightarrow x= \frac{-5+1}{2}=\boxed{-2}\\\\
2x - 1 = -1 \Longrightarrow 2x = -1+1\Longrightarrow x= \frac{-1+1}{2}=\boxed{0}\\\\
2x - 1 = 1 \Longrightarrow 2x = 1+1\Longrightarrow x= \frac{1+1}{2}=\boxed{1}\\\\
2x - 1 = 5 \Longrightarrow 2x = 5+1\Longrightarrow x= \frac{5+1}{2}=\boxed{3}\\\\
\Longrightarrow ~~\boxed{A=\{-2;~0;~1;~3\}}[/tex]
