5. (10 points) Among the two-digit numbers that can be divided by the sum of their digits, there are $\qquad$ odd numbers.

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【Analysis】Obviously, an odd number can only be divisible by an odd number, so the sum of the digits of this odd number must be odd. Since the unit digit of this two-digit number is odd, the tens digit can only be even, which means the tens digit of this odd number can only be $1, 3, 5, 7, 9$, and this odd number cannot be a prime number, so we need to exclude prime numbers, and finally determine the number of odd numbers.

【Solution】Solution: According to the analysis, the tens digit of the odd number that meets the condition can only be: $2, 4, 6, 8$. After excluding prime numbers, only the following remain: $21, 25, 27, 45, 49, 63, 65, 69, 81, 85, 87$. After checking one by one and excluding $25, 49, 65, 69, 85, 87$,

Therefore, the odd numbers that meet the condition are: $21, 27, 45, 63, 81$, a total of 5.
So the answer is: 5.