So by flashing the HD5850 with a HD5870's BIOS file you are effectively tricking the card into thinking it's a HD5870? Does this unlock any extra processors (5870=1600 5840=1440) or just it just increase the maximum clock rate?
No we haven't flashed any bios', just edited the config of afterburner to enable the voltage control to work.
To modify the database to make it use your card settings try to close Afterburner, open your profile file with notepad (VEN_1002&DEV_6899&SUBSYS_0B001002&REV_00&BUS_1&DE V_0&FN_0.cfg stored into .\Profiles subfolder into application folder), and add the following text to it:
[Settings]
VT1165_Defaults = 17 33
Then start Afterburner again and see if it helps. It is important to add that if you have UAC enabled, then you must temporarily disable it prior to editing the file.