I also thought to Rondell 0058, I have no knowledge of them being fitter OEM on the E39 at some point but it might be.
If that's the case you might be looking at an ET20 8J for the front and ET26 9J for the rear, if I am right and they are ROD wheels the it's ET13 8,5J at the front and ET15 10J

!!! at the rear.
Having the facelift you will be totally fine at the rear, with about 20mm of extra stickout, but they will not fit at the front, unless you want to go outlaw and possibly install some limiter for the steering.