To find the difference in miles Jake runs on each day, we need to subtract the distance he runs on Tuesday from the distance he runs on Monday.
Jake runs \( 7\sqrt{6} \) miles on Monday and \( 5\sqrt{6} \) miles on Tuesday. We calculate the difference as follows:
\[ 7\sqrt{6} - 5\sqrt{6} \]
Since both terms have the common factor \( \sqrt{6} \), we can factor it out:
\[ = (7 - 5)\sqrt{6} \]
Now, we simplify \( 7 - 5 \):
\[ = 2\sqrt{6} \]
Thus, the difference in miles run each day is
\[ \boxed{2\sqrt{6}} \text{ miles.} \]