[Wonkydog]

Have you got 16's at the moment?
M5 wheels will fit - just. If you can get hold of a set of second hand ones, go for it. The inner rim is 1cm closer to the shock absorber.

It's not just the offset, E39 wheels have a unique hub diameter that makes it difficult to fit rims from other models (E34/E36 etc)

 

[Wonkydog]

Rims are bigger (circumference and width)

Circumference difference is taken up by changing the tyre profile ie going from a 225 55 16 to 225 50 17 (for example) to keep the speedo accuracy.
Middle figure (55/50) is the percentage of sidewall height to tyre width.

Width change is different, one or both edges of a wheel will be a different distance away from the centreline - (not the surface that sits flush with the brake disc) as you look at the wheel front to back.

This is the ET figure. Since a wider wheel is going on to a car body built for smaller wheels - gaps will get tight.
Hope this makes sense.