Good Lord, it has to be extremely difficult to attempt to remove it from the top given that it's hard enough from underneath the vehicle with all the leverage one has from that position. I didn't even have to lift the vehicle; there was sufficient space to tackle it from underneath (mine is factory height with 19" wheels).

Yep, I removed both the cables first before attempting to remove the alternator. I removed both the cables from underneath- it was fairly easy. Make sure the battery is disconnected! I think it's 10mm nut for the battery cable. The data/signal cable was relatively a little bit challenging but I managed to get it out by first unclipping it from underneath the vehicle (which for me didn't quite remove it from the clip), then from the top using a screw driver kinda pushed the connection out. Be careful as you do this so that the plastic doesn't break.

It takes patience. Good luck!

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'05 E53 X5 4.4i, '97 E39 528, '07 E92 335i, '16 F86 X6M.