4. (5 points) If a two-digit number divisible by 5 is neither divisible by 3 nor by 4, its 97 times is an even number, and the tens digit is not less than 6, then this two-digit number is $\qquad$
【Analysis】Obviously, if a number is divisible by 5, then its unit digit can only be 0 or 5. Since its 97 times is an even number, it indicates that this two-digit number is an even number, so we can conclude that the unit digit of this two-digit number is 0. The tens digit is no less than 6, so it can only be $6, 7, 8, 9$. Since it cannot be divisible by 4, the tens digit cannot be $6, 8$, so the tens digit can only be 7 or 9. Since it cannot be divisible by 3, the tens digit can only be 7.

【Solution】Solution: According to the analysis, if a number is divisible by 5, then its unit digit can only be 0 or 5. Since its 97 times is an even number, it indicates that this two-digit number is an even number, so we can conclude that the unit digit of this two-digit number is 0. The tens digit is no less than 6, so it can only be $6, 7, 8, 9$. Since it cannot be divisible by 4, the tens digit cannot be $6, 8$, so the tens digit can only be 7 or 9. Since it cannot be divisible by 3, the tens digit can only be 7.

In summary, this two-digit number is 70,
The answer is: 70.