You need an alternator or the voltage regulator. The new (rebuilt or new) alternator comes with the regulator, or you can replace the regulator by itself.

Somebody said that the regulator is 15 dollars. That's not entirely true, indeed it is mostly false, but the regulator is far less than the entire alternator.

The regulator collects the AC electricity that is generated, and converts it to DC that the car can use. The conversion is done with a circuit called a bridge rectifier that is built out of a series of 4 diodes. One or more of the diodes can fail, and the rectifier circuit breaks down. The regulator also uses a pair of brushes that ride on the commutator (shaft) of the alternator, and the brushes can wear out.

When you have the alternator out, the place where the various wires attach is the regulator, and two more screws will have it out.

Yea I said $15, just because I forgot. But this is it at auto warehouse.
BMW X5 Voltage Regulator - Free Shipping - Bosch, OES Genuine

That being said. Get the oe BMW one even cheaper through Craig at Openroad BMW. It is a fraction of the cost of an alternator.

Unless the engine is running, you know nothing about the status of the alternator.

Start the engine and measure the voltage, you should see something in the range of 14.5v, give or take a few tenths.

Alternator is not rebuildable, gotta get a new one...
In the process of removing it, the brittle nipple on the plastic connector where the small hose connects the upper rad hose and expansion tank broke off, not sure if I should glue it back on until I tackle the whole cooling system?

Power steering hoses leak like crazy...oh well...one job at a time.