the only documentation on the sport button itself (not the shifter) states it affects suspension only. In my opinion this is true because if you don't get the sports package (adaptive drive) then you don't get the sport button. Adaptive drive only affects the suspension (also documented).

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'08 X5 3.0si - Alpine White / Saddle Brown interior
Specs: Sport Pkg, Premium Pkg, Tech Pkg, Comfort Access, Aero Kit, Style 433 staggered 20s on Conti DWS
Mods: Carbon 35 tint, LED angel eyes, GP Thunder 7500k fogs, H&R 20mm/25mm spacers, clear reflectors, gunsmoke-tinted taillights
Coded: Digital speedo, windows/sunroof/tailgate close via keyfob

X5 pics at Flickr