39830

I started this problem with the largest odd number as 9877.After this,I calculated my largest even number as 9864.Then,instead of using 5001 as my closest number to 5000,I used 5012 and used 1035 as my smallest multiple of 5. This left me with the digits 2346. I rearranged the numbers to make 6432 as the largest multiple of 3.Therefore my result was:9877,9864,6432,1035 and 5012.

Some rules are:Do most of them in descending order and try to begin the smallest multiple of 5 with 1.