5. According to national regulations, only adults who are 18 years old or older but not over 70 years old are eligible to apply for a motor vehicle driver's license. Li Ming, a sixth-grade student, said: "My dad has a driver's license, and the product of his age and his birth month and day is 2975." How old is Li Ming's father?
5. According to national regulations, only adults who are 18 years old or older and no more than 70 years old are eligible to apply for a motor vehicle driver's license. Li Ming, a sixth-grade elementary school student, said: "My dad has a driver's license, and the product of his age and his birth month and day is 2975." How old is Li Ming's father?
【Analysis】Li Ming, a sixth-grade elementary school student, is around 12 years old. The legal marriage age is 22 years old, so his father's age must be over 30 years old. Age number $\times$ birth month number $\times$ day number $=2975$, then factorize 2975, i.e., 2975 $=5 \times 5 \times 7 \times 17$, and discuss based on the prime factors.
【Solution】Solution: Li Ming, a sixth-grade elementary school student, is around 12 years old. The legal marriage age is 22 years old, so his father's age must be over 30 years old.
$$
2975=5 \times 5 \times 7 \times 17
$$

To combine the four factors 5, 5, 7, 17 into birth month, day, and age, since his father's age must be over 30 years old, it can only be $5 \times 7=35$ years old, which fits the context; the maximum month number is 12, so the month number is 5, and the day number is 17;

Answer: Li Ming's father is 35 years old.