This is always an odd one to me, but I'm definely not an expert, only somebody who has spent far too much time reading up about it :roll:
With the Mobil oils, the 0w-40 is a "Mobil 1" oil (along with the Mobil 1 5w-50 and Mobil 1 10w-60) whereas the the 5w-40 isn't. You get the distinct impression if you do a little research, including reading Mobil's own description of their oils, that the Mobil 1 range is their "premium" range made from the same high quality basestocks, anti-wear, anti-sludge, anti-acidity additive package and they seem to offer pretty impressive HTHS viscosity (anti-shear) compared to other Porsche A40 approved oils.
If your indie is suggesting the Mobil 5w-40 because it's "thicker", it doesn't really stack up for me because at operating temp, the "-40" is the same, it's only when cold that the "5w" is thicker than the "0w" but unless your car is leaking oil when cold/stationary, I can't see the benefit of the 5w over a 0w :?
If you want a thicker oil because you've racked up a few miles and believe that the greater internal clearances means thicker is better and you want a Porsche A40 approved oil, then Mobil 1 5w-50 is an option. My car has done 51k miles and I'm leaning in that direction for its next change, an OPC will use it if asked and many default to it for older cars.
If you're not concerned about staying with Porsche A40 approved oil and want to go up a level in quality to a racing oil and also go thicker, then there are a few options, such as a Motul 5w-50 ester-synthetic oil or of course the Millers NFS nano oils that lots of people on here use and Hartech will recommend too, it comes in 5w-40, 10w-50 and 10w-60.