What YEAR and MODEL M5 do you have? Do you know there are like 4 versions
of M5s - E28, E34, E39 and E60?

It sounds like 02 sensor problem that could be related to an intake manifold
leak. Other related problem I saw was oil that leak in spark plug hole.(leak
cause by bad cyl. head cover gasket) That kind of leak can kill ignition
coils as well so check it out.
So I'll check first---oil in spark plug recess and change inner and outer
head cover gaskets if required and don't forget the round rubber seal for
the fasteners, they dry out pretty fast. You did not specified mileage/km
but may be it's time for new plugs anyway...
2---intake leak -- check all rubber line/crankcase ventilation and oil
separator component. Ensure all throttle bodys are all thight (torque to
15Nm /11 lb/ft)
After being sure that both air and/or oil leak are fix and/or fine I'll go
for the  2 rearmost O2 sensor (the monitors) then the forward ones if
problem persist.
3--- lately your problem could be related to an internaly destroyed/or
clogged catalytic converter(s). That means $$$$ if out of warranty (6 years)
Note: Make sure to disconnect the batery first and then  the ECU for at
least 10 minutes before running eng. (after fixing any of those things).
That will reset the ECU  back to is normal operating setting. Internal
adjustement is done to the air mixture due to small air leak and normal wear
component, but there's a limit and you are already out of this limit. The
other way is to let the eng. idle for 30 minutes but it's a waste.
So..disconnect...fix (any of those checks and fix will take more then
10minutes)...reconnect...
run (and hopefully enjoy).
In my case (M62 eng.) things get better after changing head covers gaskets
and re-torque the intake, but still had misfire occasionaly (1-2 times a
month) but after replacing the  O2 sensors monitors everything went back to
normal...for 6 months til I changed the 2 others O2 sensors since then
(40,000 km) everything's fine and I'm running 305,000km. But a friend of
mine had to
go all the way to the cats replacement.

Good luck