Bridgestone RE003.
Please, don’t put sh*t tyres on your capable German car. There’s no coincidence that wreckers observe a good proportion of their custom from BMWs equipped with rubbish rubber!
The RE003 is reasonably priced, performs well on e60, brilliant in the wet, sticky enough yet give reasonable wear too.
The difference in grip and braking distance between a decent tyre and a cheap shitty tyre will be marked in the pedestrian you may well hit on the cheap tyres in an emergency stop. The few dollars saved won’t seem worth it, then.