To simplify the expression \( 7\sqrt{72} - 5\sqrt{2} \), we start by simplifying \(\sqrt{72}\).
\[ \sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2} \]
Now, we substitute this back into the expression:
\[ 7\sqrt{72} = 7 \times 6\sqrt{2} = 42\sqrt{2} \]
Now, we rewrite the original expression:
\[ 42\sqrt{2} - 5\sqrt{2} \]
Next, we can combine the like terms:
\[ (42 - 5)\sqrt{2} = 37\sqrt{2} \]
Thus, the simplified expression is:
\[ \boxed{37\sqrt{2}} \]