[tex]\displaystyle\\
\Big (\frac{x}{y} - \frac{y}{x}\Big) \cdot \frac{5xy}{x-y} =\\\\
=\Big (\frac{x\cdot x}{y\cdot x} - \frac{y\cdot y}{x\cdot y}\Big) \cdot \frac{5xy}{x-y} =\\\\
=\Big (\frac{x^2}{xy} - \frac{y^2}{xy}\Big)\cdot \frac{5xy}{x-y} =\\\\
=\frac{x^2-y^2}{xy}\cdot \frac{5xy}{x-y} =\\\\
=\frac{(x+y)(x-y)}{xy}\cdot \frac{5xy}{x-y} =\\\\
=\frac{5xy(x+y)(x-y)}{xy(x-y)}= \boxed{\bf 5(x+y)} [/tex]
