Light acceleration is best with a cold engine.

Could be spark knock but only on right turns indicates something else. Doesn't sound like motor mounts since it is only on right turns and when the engine is cold. On right turns the left side suspension is loaded. Suggest troubleshooting there first.

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X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas