White smoke coming from tailpipe
 

Hey guys, new to the forum new to the e60 N54. Little background on my situation Just picked this car up for $1000.00, it's in really good shape with 149k. So if I have to put some cash in I will.guy had it parked for 3 years when he parked it, it had started over heating. Wasn't/ isnt leaking coolant you could drive it for awhile and then the fail safe loud fan would kick on . Then it would later overheat . I replaced the thermostat and the coolant temp sensor, no luck. My buddy has a wrecked e90 we pulled his coolant pump out and put it in the e60 (mind you we just changed thermostat 2 days ago. Always do both -_-). So, newish waterpump. Bled thr system . Bam shes running like a top, no lights not sluggish everything seems as it should.

Now, the only thing I'm left wondering is this white smoke from my tailpipe . Its constant. any help would be most appreciated. Thanks! Here is a picture of the old coolant pump and whatever that thing is inside it.
https://cimg7.ibsrv.net/gimg/5series...ed93d9bba2.jpg
There isn't oil in the coolant .

turbos ever been replaced? probably shot by now if not.

first check if there is coolant in the oil. depending on how long the car was overheating, head/headgasket might be bad. otherwise its probably the turbos.

Oil isnt milky I dint think its head gasket. What about the possibility of it sitting and just moisture getting in the gas ? Havent put mew gas or sea foam in it yet

Do a smell test on the exhaust. Coolant smells sweet, oil smells like burned oil, condensation into cool air smells like moist exhaust.