To simplify \( 11 \sqrt{19} - 5 \sqrt{9} \), first, we can simplify \(\sqrt{9}\):
\[ \sqrt{9} = 3 \]
Now, substitute this back into the expression:
\[ 11 \sqrt{19} - 5 \sqrt{9} = 11 \sqrt{19} - 5 \cdot 3 \]
This simplifies to:
\[ 11 \sqrt{19} - 15 \]
Thus, the final answer is:
\[ 11 \sqrt{19} - 15 \]