Take the cover off the top of the engine and have a good look around.

Oil over that side of the engine is a bit odd as most of the intake/turbo etc is on the other side.

That kind of oil does look like dirty diesel intake though, the kind you find in the turbo air lines etc.
Try having a look around the intercooler connections.

Another place to look is at the EGR hoses at the top front of the engine, this is about the closest air/recycle lines to the radiator tank.
If your EGR has never been cleaned, I would also remove and clean it, as it is sure to have a lot of crude in it.

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2004 E53 X5 3.0d