The given equation is:

$\frac{x+7}{2} = \frac{5x}{3}$

To solve this, we will first eliminate the fractions by multiplying both sides by the least common denominator (LCD) of 2 and 3, which is 6.

Step-by-step solution:

1. Multiply both sides by 6 to eliminate the denominators: $6 \times \frac{x+7}{2} = 6 \times \frac{5x}{3}$

2. Simplify both sides: $3(x + 7) = 2(5x)$

3. Distribute the numbers on both sides: $3x + 21 = 10x$

4. Move all terms involving $x$ to one side of the equation: $21 = 10x - 3x$

5. Simplify: $21 = 7x$

6. Solve for $x$: $x = \frac{21}{7} = 3$

Thus, the solution is $x = 3$.

Would you like more details on this solution or have any further questions?

Here are 5 related questions for further practice:

1. How would you solve $\frac{x + 4}{3} = \frac{2x}{5}$?
2. What is the solution to $\frac{3x - 2}{4} = \frac{5x}{6}$?
3. How can you simplify an equation with fractions on both sides?
4. What happens when the variable appears on both sides of an equation?
5. Can you find the solution to $\frac{x - 5}{7} = \frac{x}{3}$?

Tip: Always check your solution by substituting the value of $x$ back into the original equation.