jmc

Multiply both sides of the given equation by both denominators to obtain $$\begin{array}{rl}5(10x-3y)& =3(13x-2y)⟹\\ 50x-15y& =39x-6y.\end{array}$$ Collect like terms by adding $15y$ and $-39x$ to both sides to obtain $11x=9y$. Finally, divide both sides by $11y$ to find that $\frac{x}{y}=\boxed{\frac{9}{11}}$.