1 2 3 4 5
A | | | | | |
B | | | | | |
C | | | | | |
D | | | | | |
E | | | | | |

1. The sum of each column is odd
   
2. The sum of each row, except C, is even
   
3. The sum of row A is not greater than the sum of any other row
   
4. The sum of the diagonal E1 to A5 is less than that of the diagonal A1 to E5
   
5. A4 + B4 > C4 + D4 + E4
   
6. A1 + B1 = D1 + E1
   
7. A1 > E1
   
8. A1, A3 and B1 are all prime numbers
   
9. (A3 + E3) is a prime number
   
10. A5, D1, D3 and E1 are all squares
    
11. B2, C2 and D2 are ascending consecutive numbers
    
12. B3, C3 and D3 are ascending consecutive numbers
    
13. B5 + D5 = A5 + C5
    
14. (C1)² + (C5)² = (E3)²
    
15. C5 is a two digit number
    
16. D5 is a multiple of E5
    
17. E1 + E3 = E2 + E4 + E5

i stumbled upon this site while i was googling something else, and this puzzle grabbed my attention.  here's the solution that i came up with.  (great puzzle!)

07,11,02,17,01
13,19,23,22,03  
09,20,24,14,12 
16,21,25,18,10
04,08,15,06,05