RepairPal Certified shops can diagnose and repair your 2001 BMW 530i. They provide transparent pricing with a minimum 12-month or 12,000-mile warranty on repairs and services.
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check to see if it has a superseded fan speed resistor fitted.
old style has approx. 15 fins while the new style has approx. 40
if old style fitted replace fan speed resistor
out of all bmws, e39 (your model) are the easiest
http://www.bimmerfest.com/forums/showthread.php?t=143393
I followed these instructions and reparied myself. Longest time was waiting for the part as I did not want to pay the dealer 2x markup.