To solve the equation \( 5(2x + 3) = 7x - 3 \), we first distribute the \( 5 \) on the left side:
\[ 5 \cdot 2x + 5 \cdot 3 = 10x + 15 \]
So the equation becomes:
\[ 10x + 15 = 7x - 3 \]
Next, we want to isolate \( x \) by getting all the \( x \) terms on one side of the equation. We can subtract \( 7x \) from both sides:
\[ 10x - 7x + 15 = -3 \]
This simplifies to:
\[ 3x + 15 = -3 \]
Now we subtract \( 15 \) from both sides to further isolate the \( x \) term:
\[ 3x = -3 - 15 \]
This simplifies to:
\[ 3x = -18 \]
Next, we solve for \( x \) by dividing both sides by \( 3 \):
\[ x = \frac{-18}{3} \]
This simplifies to:
\[ x = -6 \]
Thus, the solution to the equation is:
\[ \boxed{-6} \]