To solve the equation:

$\frac{3}{x} = \frac{1}{5}$

Let's cross-multiply to get rid of the fractions:

$3 \times 5 = 1 \times x$

This simplifies to:

$15 = x$

So, the solution is:

$x = 15$

Would you like further details or have any questions?

Here are some related questions for further exploration:

1. How would you solve $\frac{5}{x} = \frac{2}{3}$?
2. If $\frac{4}{x} = \frac{2}{7}$, what is the value of $x$?
3. What happens if both sides of the equation $\frac{3}{x} = \frac{1}{5}$ are multiplied by $x$ directly?
4. How can we verify that $x = 15$ is correct in the original equation?
5. How does solving $\frac{3}{x} = \frac{1}{5}$ differ from solving equations without fractions?

Tip: Cross-multiplying is a quick and effective way to solve equations involving fractions.