5. If 7 is subtracted from the thought three-digit number, the resulting difference will be divisible by 7; if 8 is subtracted, the resulting difference will be divisible by 8; if 9 is subtracted, the resulting difference will be divisible by 9. What is the smallest possible number thought of?
5. The intended number is divisible by $7, 8, 9$. The smallest number divisible by 7, 8, and 9 is $7 \cdot 8 \cdot 9=504$. This number meets the requirement of the problem.