You had "greater than 3000", but all 5-digit numbers are greater than 
3000, so I changed it to 30000.

Choose the last (5th) digit even as 4 or 8.  That's 2 ways.
 
Choose the first digit odd as 3 or 5 (not 1, since it has to be greater 
than 30000).  That's 2 ways.

Choose the second digit as any of the 3 that are left.  That's 3 ways

Choose the third digit as either of the 2 that are left.  That's 2 ways.

Choose the fourth digit as the only one that is left.  That's 1 way.

Answer 2×2×3×2×1 = 24

Here they all are:

 1. 31458
 2. 31548
 3. 31584
 4. 31854
 5. 34158
 6. 34518
 7. 35148
 8. 35184
 9. 35418
10. 35814
11. 38154
12. 38514
13. 51348
14. 51384
15. 51438
16. 51834
17. 53148
18. 53184
19. 53418
20. 53814
21. 54138
22. 54318
23. 58134
24. 58314

Edwin