5. We will call a number greater than 25 semi-prime if it is the sum of some two different prime numbers. What is the maximum number of consecutive semi-prime numbers that can be semi-prime?
5. Note that an odd semiprime number can only be the sum of two and an odd prime number.

Let's show that three consecutive odd numbers $2n+1, 2n+3, 2n+5$, greater than 25, cannot all be semiprimes simultaneously. Assume the opposite. Then we get that the numbers $2n-1, 2n+1, 2n+3$ are prime, and all of them are greater than 3. But one of these three numbers is divisible by 3. This leads to a contradiction. Therefore, three consecutive odd numbers $2n+1, 2n+3, 2n+5$, greater than 25, cannot all be semiprimes simultaneously.

Note that among any six consecutive natural numbers, there are three consecutive odd numbers, so there cannot be more than five consecutive semiprime numbers. Five consecutive numbers can be semiprimes; for example, $30=17+13, 31=29+2, 32=19+13, 33=31+2, 34=23+11$. There are other examples as well.

Answer: 5.