\(\dfrac{5}{x}-\dfrac{y}{3}=\dfrac{1}{6}\)
\(\Rightarrow\dfrac{5}{x}=\dfrac{1}{6}+\dfrac{y}{3}\)
\(\Rightarrow\dfrac{5}{x}=\dfrac{1}{6}+\dfrac{2y}{6}\)
\(\Rightarrow\dfrac{5}{x}=\dfrac{1+2y}{6}\)
\(\Rightarrow x\left(1+2y\right)=30\)
\(\Rightarrow x;1+2y\in U\left(30\right)\)
\(U\left(30\right)=\left\{\pm1;\pm2;\pm3;\pm5;\pm6;\pm10;\pm15;\pm30\right\}\)
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