Answer
$\dfrac{xy}{5y+2x}$
Work Step by Step
The given expression, $
\dfrac{5x^{-1}-2y^{-1}}{25x^{-2}-4y^{-2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{5}{x}-\dfrac{2}{y}}{\dfrac{25}{x^2}-\dfrac{4}{y^2}}
\\\\=
\dfrac{\dfrac{5y-2x}{xy}}{\dfrac{25y^2-4x^2}{x^2y^2}}
\\\\=
\dfrac{5y-2x}{xy}\div\dfrac{25y^2-4x^2}{x^2y^2}
\\\\=
\dfrac{5y-2x}{xy}\cdot\dfrac{x^2y^2}{25y^2-4x^2}
\\\\=
\dfrac{5y-2x}{xy}\cdot\dfrac{x^2y^2}{(5y-2x)(5y+2x)}
\\\\=
\dfrac{\cancel{5y-2x}}{\cancel{xy}}\cdot\dfrac{\cancel{xy}\cdot xy}{(\cancel{5y-2x})(5y+2x)}
\\\\=
\dfrac{xy}{5y+2x}
.\end{array}
