number is greater than 50 and less than 100. you can make exactly 5 different rectangles with a mystery numbers of tiles. its prime factorization consists of only one prime number. whats my number

To find the mystery number, we will first list out the prime numbers between 50 and 100:

53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Now, let's go through each of these numbers and see if we can make exactly 5 different rectangles with a mystery number of tiles using them:

1. For 53:
- We can have a rectangle with dimensions 1 x 53 (using 53 tiles).
- We can have a rectangle with dimensions 53 x 1 (using 53 tiles).
- We cannot make any additional rectangles with the given condition.

2. For 59:
- We can have a rectangle with dimensions 1 x 59 (using 59 tiles).
- We can have a rectangle with dimensions 59 x 1 (using 59 tiles).
- We cannot make any additional rectangles with the given condition.

3. For 61:
- We can have a rectangle with dimensions 1 x 61 (using 61 tiles).
- We can have a rectangle with dimensions 61 x 1 (using 61 tiles).
- We cannot make any additional rectangles with the given condition.

4. For 67:
- We can have a rectangle with dimensions 1 x 67 (using 67 tiles).
- We can have a rectangle with dimensions 67 x 1 (using 67 tiles).
- We cannot make any additional rectangles with the given condition.

5. For 71:
- We can have a rectangle with dimensions 1 x 71 (using 71 tiles).
- We can have a rectangle with dimensions 71 x 1 (using 71 tiles).
- We cannot make any additional rectangles with the given condition.

6. For 73:
- We can have a rectangle with dimensions 1 x 73 (using 73 tiles).
- We can have a rectangle with dimensions 73 x 1 (using 73 tiles).
- We cannot make any additional rectangles with the given condition.

7. For 79:
- We can have a rectangle with dimensions 1 x 79 (using 79 tiles).
- We can have a rectangle with dimensions 79 x 1 (using 79 tiles).
- We cannot make any additional rectangles with the given condition.

8. For 83:
- We can have a rectangle with dimensions 1 x 83 (using 83 tiles).
- We can have a rectangle with dimensions 83 x 1 (using 83 tiles).
- We cannot make any additional rectangles with the given condition.

9. For 89:
- We can have a rectangle with dimensions 1 x 89 (using 89 tiles).
- We can have a rectangle with dimensions 89 x 1 (using 89 tiles).
- We cannot make any additional rectangles with the given condition.

10. For 97:
- We can have a rectangle with dimensions 1 x 97 (using 97 tiles).
- We can have a rectangle with dimensions 97 x 1 (using 97 tiles).
- We cannot make any additional rectangles with the given condition.

After going through all the numbers, we can see that none of them satisfy the given condition of making exactly 5 different rectangles. It is possible that there is no number that meets all the criteria given.