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Решите задачу:

$\left \{ {{\frac{x}{y}-\frac{y}{x}=\frac{5}{6}} \atop {x+y=5}} \right. \; \left \{ {{\frac{x^2-y^2}{xy}=\frac{5}{6}} \atop {x+y=5}} \right. \; \left \{ {{\frac{(x-y)(x+y)}{xy}=\frac{5}{6}} \atop {x+y=5}} \right. \; \left \{ {{\frac{5(x-y)}{xy}=\frac{5}{6}} \atop {x+y=5}} \right. \; \left \{ {{6(x-y)=xy} \atop {y=5-x}} \right. \\\\6(x-(5-x))=x(5-x)\\\\6(2x-5)=5x-x^2\\\\12x-30=5x-x^2\\\\x^2+7x-30=0\\\\D=169,\\\\x_1=\frac{-7-13}{2}=-10,\; x_2=3\\\\y_1=5-(-10)=15,\; y_2=5-3=2\\\\Otvet:\; (-10,15),\; (3,2)$