2003 X5 5 speed auto harshly vibrates

[flyup123]

Hello all! I have a green ‘03 X5, and it’s been doing this since I got it a few months ago. It has the 5 speed automatic (I can’t be bothered to remember the code for it), the 4.4i, and is all-wheel drive. It starts off driving and shifting quite nice and smooth for an early 2000s slushbox, but after around ten minutes the transmission and transfer case warm up. Once this happens, it vibrates and downshifts harshly when going up a hill. If I slow down for something and press the gas pedal, it also vibrates. It feels like it’s coming from the rear of the transmission, or the transfer case. I’ve heard the transfer case is a problem when mated to the 5 speed auto, and figured you’d have a few suggestions. Thanks!