Welcome to United Bimmer. Good to hear your looking at an E39. Probably the best 5 Series ever built. If you can I would suggest trying I find a 540i if an M5 is out of your budget. The 528 uses the same M52 engine as the E36, but because of the bigger size their slower then the E36. Still very fun to drive.
Common failure points include the Rear Trailing Arm Bushings (RTAB) and the Rear Shock Mounts (RSM). As with any car a standard inspection of suspension and steering components is important. Checking to ensure the coolant system is functioning properly is important. The M52 has a plastic radiator and expansion tank that was prone to cracking. Same with the thermostat housing. The aluminum replacements are much better. Same with the water pumps. The pre-1997 ones (I think) were all plastic impeller and were prone to failure. At least with the M52 engine.