If $5^x={\left(0.5\right)}^y=1000$, then $\frac{1}{x}-\frac{1}{y}=$

$5^x={\left(0.5\right)}^y=1000$

$5^x={10}^3\Rightarrow 5={10}^{\frac{3}{x}}\to \left(1\right)$

${\left(0.5\right)}^y={10}^3\Rightarrow 0.5=0^{\frac{3}{y}}\Rightarrow 5={10}^{\frac{3}{y}+1}\to \left(2\right)$

From (1) and (2), ${10}^{\frac{3}{x}}={10}^{\frac{3}{y}+1}$

$\frac{3}{x}-\frac{3}{y}=1\Rightarrow \frac{1}{x}-\frac{1}{y}=\frac{1}{3}$