I changed my 01 4.4 waterpump (and rest of cooling sys) at about 86,000 miles.

My alternator seized up a few months later, probably around 90k miles. Left me stranded. I rode home that day in the cab of a flatbed towtruck.

Since the alternator is watercooled, you do have to partially drain the coolant when replacing it. Might save you some time doing them together.

But I obviously did them separately, and I found the alternator easier to replace then the WP. I didn't feel like I was repeating a ton of labor replacing them at different times.

The alternator is pretty expensive (think I paid 300 or 400 from autohausAZ), but getting stranded in the X5 sucks too.

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Now:
E53 4.4i Sport
E39 /// M5
back then:
E36
E30 (x2)
E21