jmc

We first combine the two fractions with $x$ in the denominator to give $\frac{3}{x}-\frac{3}{5}=\frac{1}{5}$. Adding $\frac{3}{5}$ to both sides gives us $\frac{3}{x}=\frac{4}{5}$. Cross-multiplying this equation (or multiplying both sides by $5x$) gives $4x=15$. Dividing both sides of this equation by $4$ gives us $x=\boxed{\frac{15}{4}}$.