The equation you provided is:

$\frac{5}{7} = \frac{x}{3}$

To solve for $x$, we can use cross-multiplication. Here's the process:

1. Cross-multiply: $5 \cdot 3 = 7 \cdot x$

2. Simplify: $15 = 7x$

3. Solve for $x$ by dividing both sides by 7: $x = \frac{15}{7}$

So, the value of $x$ is:

$x = \frac{15}{7}$ or approximately $x \approx 2.14$.

Would you like more details or have any questions?

Here are 5 related questions:

1. How would you solve $\frac{a}{b} = \frac{c}{d}$?
2. What happens if you reverse the numerators and denominators in a proportion?
3. How does cross-multiplication work with fractions in algebra?
4. What would happen if one of the values were negative in this equation?
5. How can we check if the solution is correct after solving the equation?

Tip: When working with proportions, always ensure you simplify as much as possible before cross-multiplying to avoid large numbers.