5W30 (especially Mobil 1) is way too thin for an E36 M50 engine.  It
will cause inadequate actuation of the VANOS due to low oil pressure.
Been there...  done that.

I use a 5W40 in colder weather (Shell Rotella T Synthetic is good) and
up to Mobil 1 20W50 in the summer months.

I can't imagine why you would need 50w oil. The recommended oil is 10w30,
but lots of guys around here -- on this board -- use 5w30 synthetic.

The first of the two numbers indicates how the oil will behave in cold
weather, and the second number says how the oil will behave when it gets
hot. Dino oils work best when the spread is relatively narrow -- 10w30
should hold up better than 10w40, although the 10w40 will protect in a
broader range of temperatures (having said that, it is seldom that one would
need protection to minus 20 and plus 100+ in the same load of oil, so 10w40
is not really very useful as a practical matter).

Synthetic blends do not have the viscosity breakdown issues of dino oil, and
the wider range -- 5w30 -- seem to fit most of the planet in a year around
application. There is a 0w30 if you look hard enough, but unless your
nipples break off when you go outside, I don't think you need to expend the
energy looking for it.

what are your recommendations?

What do you think about using  Fuchs oil 5w50 (sythetic oil)?

My engine has about 140 000 km.