39835

I started with 9977 as my largest odd number because they were the highest odd number.Then I chose the numbers 8866 because they were the highest even numbers.After I chose the numbers 5001 for the closest to 5000 because it was 1 off.I was left with 43321245.Then the smallest multiple of five so it has to end in 0 or 5 then I chose 1245.Then the last box was smallest multiple of 3 so it had to be 4332 as they are the only numbers left and they worked.