Plugs and coils seem to be a good place to start! coils if the problem still persists! (any OBD2 codes?? )
previous owner using premium fuel as well??

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2003 X5 3.0i (02/2003) sport package, Sapphire black metallic / Black Dakota Sport seats. compass mirror retrofit, trailer hitch retrofit, Prodigy P2 trailer brake controller installed, PDC retrofit, Lumbar support retrofit. heated rear seats retrofitted. Running boards retrofitted and subwoofer install in progress. 4.8is Brakes installed front and back. Bluetooth TCU installed, Rear Fog lights installed. Retrofitted reclining rear seat backs.