To solve the equation
\[ \frac{x - 3}{2} = \frac{x + 3}{5}, \]
we can start by cross-multiplying to eliminate the fractions. This gives us:
\[ 5(x - 3) = 2(x + 3). \]
Now, distribute both sides:
\[ 5x - 15 = 2x + 6. \]
Next, we will isolate \(x\) by getting all the \(x\) terms on one side and the constant terms on the other side. Subtract \(2x\) from both sides:
\[ 5x - 2x - 15 = 6, \] which simplifies to
\[ 3x - 15 = 6. \]
Now, add 15 to both sides:
\[ 3x = 21. \]
Finally, divide by 3:
\[ x = 7. \]
Thus, the solution to the equation is
\[ \boxed{7}. \]