\(\left\{{}\begin{matrix}\dfrac{x}{y}-\dfrac{y}{x}=\dfrac{5}{6}\\x^2-y^2=5\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}6x^2-6y^2=5xy\\x^2-y^2=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x^2-6y^2=5xy\\6x^2-6y^2=30\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}0=5xy-30\\6x^2-6y^2=30\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5xy=30\\6x^2-6y^2=30\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{30}{5y}\\6\left(\dfrac{30}{5y}\right)^2-6y^2=30\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{30}{5y}\\\dfrac{216}{y^2}-6y^2=30\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{30}{5y}\\216-6y^4=30y^2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{30}{5y}\\y=2\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=3\\y=2\end{matrix}\right.\)
