Double check all grounds

Remove them, clean, then reassemble including the one under the vehicle by the fire wall by your left foot area.
Test your alternator at the B+ battery post (the fat cable at the back of the Alt) Read volts with key on, engine at idle, 1500 and 2500 RPM steady for 15 secs. Does the volt reading fluctuate more than 1Volt?

Results: With key on you should get battery voltage. see chart above. You can NOT get an alternator to function properly with a bad or discharged battery.
If yes, bad regulator, brush contact to spinning parts. In other words, defective rebuilt unit.

Do a drop test on the battery cables in the trunk YES grounds and Bat + also. Many have chased problems only to discover the battery positive cable had been fired off by a hit. See positive cable view above.

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2005 X5 4.8IS
The Blue ones are always FASTER....

Current Garage:
2005 X5 4.8is
2002 M5 TiSilver
2003 525iT
1998 528i
Former Garage Stable Highlights
2004 325XiT Sport
1973 De Tomaso Pantera, L Model
1970 Dodge Challenger T/A 4 sp Alpine White
1970 Dodge Challenger T/A 4 sp GoManGo Green
1971 Dart Sport, “Dart Light” package
1969 Road Runner 383
1968 Ply Barracuda 340S FB Sea-foam Green