The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1, 3, 5, 7, 9 without repetition, is

We need to count numbers strictly between 5000 and 10000 formed using the digits 1, 3, 5, 7, 9 without repetition.

The numbers must be 4-digit numbers from 5001 to 9999. Since all available digits are odd and nonzero, every such arrangement gives a valid number.

For the number to be between 5000 and 10000, the thousands digit must be 5, 6, 7, 8, or 9. From our available digits {1, 3, 5, 7, 9}, the valid first digits are 5, 7, and 9 — giving 3 choices.

After choosing the first digit, we have 4 remaining digits and 3 remaining positions.

Number of ways = $$4 \times 3 \times 2 = 24$$

Total = $$3 \times 24 = 72$$

The correct answer is Option D: 72.