When replacing the M5’s front brakes it took me a little longer than I might have hoped to locate the brake fluid reservoir, so this is a quick blog post to address that in the hope that someone else finds it helpful. As you stare at the engine under the bonnet, it’s under the driver’s side pollen filter, as indicated by the arrow below:

To gain access, undo the plastic clips just to the right of that arrow to free it from the ducting. Also unclip the housing lid – there’s a metal bar running along the front that holds the lid in place. A certain amount of wrestling should reveal the reservoir: