Vanos? or hopefully a vacuum leak of some sort but either of those should throw a code.
If you manually shift, what happens at 2500 rpm in other gears?

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2001 x5 3.0 (sold with broken motor), 1990 e30 M3, 1991 318is, 2002 325i, 2008 335i Dinan stage 3 6 speed,