Thanks for the input. I've never seen Pentosin before but you're
right, Pentosin CHF7.1 is listed by BMW as their recommended steering
system fluid. But a quick check on the Internet picked up a
description of CHF7.1 as being green in colour. Is that right?
Otherwise, it is Dextron III in my car.

I looked in the last E39 manual (for N. America) and there is no
mention of what the owner should use. It seems to suggest you have the
garage do it... not a good idea as Dave pointed out.