How to Replace a Water Pump on an E39 BMW 5-Series (6-cylinder) ↗
Cooling-overhaul style DIY for E39 525i/528i/530i: thermostat housing off, pump driven out with two M6 bolts, then pump, pulley and housing refitted in a criss-cross pattern; includes a video and a parts list. Not difficult, but many steps.
Tools mentioned: Sockets, two 10 mm/M6 bolts, torque wrench, drain pan
Coolant temperature sensor 13621433077 is in the article's parts list (plugs into the thermostat housing).