Oki Doki, get the bonnet open and clean around the filter housing, best not get dirt in there. Unlike the E32, the E38 filter can be removed without unscrewing anything, just clips all round. Undo the two clips on the connection between the filter housing and the MAF, the other clip cannot be seen but it is quite accessible:

Remove the air temperature sensor (pre-facelift only):

Remove the clips around the filter housing:

Remove the sensor wire from the little clamp on the RHS of the housing:

The whole assembly can now be lifted up.....a slight pull away from the MAF will allow it to pop off the big 'O' ring. Yes, that's a cigarette end in there:

New filter in, make sure it correctly sits in the recess or the cover will not go on again properly:

Apply some silicone grease to the big 'O' ring:

Push the assembly over the 'O' ring to start with and make sure it has properly seated. After that it is just a case of clipping everything back on again............