What works
single player, movies

What does not

everything works flawlessly after the settings below applied

also see solution for camera moving by mouse bug:

http://bugs.winehq.org/show_bug.cgi?id=14025

What was not tested
multiplayer

Additional Comments

Problem was screen flickering
Solution:

Settings can be changed manually, especially useful if game doesn't starts or screen flickes. To reset the settings, just delete the configuration directories, no need to reinstall the game.

HoMM5 doesn't use the Windows registry. Settings are stored in directories

/My Games/Heroes of Might and Magic V/Profiles//user.cfg

/My Games/Heroes of Might and Magic V/Hammers of Fate/Profiles//user_a1.cfg

/My Games/Heroes of Might and Magic V - Tribes of the East/Profiles//user_a2.cfg

edit the file, change setting "gfx_ban_lags" to 1:
setvar gfx_ban_lags = 1

try other "gfx_..." settings to make it work

Works well with Wine's internal DX9, also works with official DX9c installed with winetricks.
Used with ATI 13.1 legacy driver.