13. (6 points) Given the five-digit number $\overline{54 \mathrm{a} 7 \mathrm{~b}}$ can be simultaneously divisible by 3 and 5, the number of such five-digit numbers is $\qquad$.
【Solution】Solution: According to the problem, the five-digit number $\overline{54 a 7 b}$ is divisible by 5, so the unit digit is 0 or 5. Then, based on the characteristic of being divisible by 3, determine the digit in the hundreds place, (1) If the unit digit is 0, the hundreds place can be 2, 5, or 8, (2) If the unit digit is 5, the hundreds place can be 0, 3, 6, or 9. Therefore, the five-digit number $\overline{54 a 7 b}$ could be $54270, 54270, 54870, 54075, 54375, 54675, 54975$, a total of 7.

Therefore, the answer is: 7.