I don't know about your 5 Series, but I have a 3 Series with the same motor, and it has been almost completely trouble free in over 100,000 miles (California). I bought my car with about the same miles as your car, and before long the plastic radiator tank broke on a narrow mountain road with no pull outs. I limped my car to the top of the hill after stopping several times to let it cool off. From the failure point to the top of the hill was only about 5 miles, and three stops. From the top of the hill, I switched the motor off and coasted to the bottom, about 7 miles, where I was able to get a tow truck to take me home.
The limping part proved to be more hazardous that I expected, and I damaged the head. I bought my car below current market value, but the repairs brought me back to market value for arguably a nicer car, but I have had no further troubles. I have replaced the front brake pads a couple of times and the front rotors once, and the rear pads once. Other than these normal repairs and the regular maintenance, the car has not cost me a dime after fixing the radiator and damaged head.
You need to look at the radiator and determine if it has plastic tanks. If it does, and most do, then you need to check the inlet (top) hose and fitting to see if the plastic is strong. My inlet tube physically broke completely off and the engine pumped all of the coolant out onto the ground. If you can catch this before it breaks, you can avoid potential damage to the head.
I bought my '94 in 2000 with 105,000 miles. It just turned 210,000. I get
25mpg or better on every tank of gas with combined city and freeway driving and doing mostly 80+ on the freeway. I can safely say that I never do less than 70 on the freeway unless traffic demands, and when traffic permits, I do 80 or better. If I could clamp my velocity at 70, I'm sure my mileage would climb to about 30mpg.My BMW has been the most pleasurable auto I have ever owned, with the possible exception of my modified Jeep that goes places vehicles are seldom asked to go.