To solve the equation \( 5(2x + 3) = 7x - 3 \), we start by distributing the 5 on the left side:
\[ 5 \cdot 2x + 5 \cdot 3 = 7x - 3 \]
This simplifies to:
\[ 10x + 15 = 7x - 3 \]
Next, we want to isolate \( x \). We can do this by subtracting \( 7x \) from both sides:
\[ 10x - 7x + 15 = -3 \]
This simplifies to:
\[ 3x + 15 = -3 \]
Now, we subtract 15 from both sides:
\[ 3x = -3 - 15 \]
This simplifies to:
\[ 3x = -18 \]
Finally, we divide both sides by 3:
\[ x = \frac{-18}{3} = -6 \]
So, the solution is:
\[ \boxed{-6} \]
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