To solve the equation \( 7(2a - 3) - 5a = -3 \), we will start by distributing the 7:
\[ 7(2a) - 7(3) - 5a = -3 \]
This gives us:
\[ 14a - 21 - 5a = -3 \]
Next, we can combine like terms on the left side:
\[ (14a - 5a) - 21 = -3 \]
This simplifies to:
\[ 9a - 21 = -3 \]
Now, we will isolate the term containing \( a \) by adding 21 to both sides:
\[ 9a = -3 + 21 \]
This simplifies to:
\[ 9a = 18 \]
Next, we will solve for \( a \) by dividing both sides by 9:
\[ a = \frac{18}{9} \]
This simplifies to:
\[ a = 2 \]
Thus, the solution to the equation is:
\[ \boxed{2} \]