That's not a regular 5-series with 21" wheels...it's an Alpina B5 with 19" wheels.
The new Alpina B5S has 20" wheels with 245/35 ZR20 front and 285/30 ZR20 rear. It's such a tight fit at the rear that on the Touring version they don't offer the 20" wheels.
I think 21" wheels is going to be a tight fit.