First off all, kudos for having the towing guy sign for it. Lots of people will forget about that in a stressful situation, and loose their case before it even started.

When I just had my 2010 3.5 diesel I did notice a burning smell from underneath the car. It was so bad I even came back from watching the world cup final at my friends house to check on it. Called the BMW shop the next dy and told me its the car burning off particles. It did not smell plastic like. (and being a RC racing guy, burning many esc, I do know that smell) . more like a paper lit on fire.

Never smelled it again.

Good luck and hopefully you will be on the road soon again.

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2010 X5 3.0D Premium - Premium sound - Executive - Sports - Rear DVD -Running boards - Tech package