As has been mentioned before, Volkswagen approval is what matters. Both VW 502 00 and 504 00 are fine for your 2.5. You could probably also use VW 511 00 oil in your Jetta, but it's more expensive and not needed at all. It's kind of a '0W-40/5W-40 version' of VW 504 00.
VW 502 00 is for gas engines, while VW 505 00 is specced for (non-DPF) Diesels. Similar with VW 504 00 (gas) and 507 00 (DPF equipped) Diesels. To make things complete, VW 508 00/509 00 is low-viscosity 0W-20 grade and NOT backwards-compatible.
Had a 2013 Jetta with the 2.5L. Ran 5W-30 Havoline High Mileage that is a semi-synthetic blend through it on multiple occasions for a 5K OCI. Ran fine and the one oil analysis I did showed no cause for concern
If running 10K mile OCI's , I would definately say stick to the VW spec stuff.
I service buddy's '10 Jetta and '08 Porsche for a couple years now, told him to buy 0w-40 whichever is on sale, be it Edge, M1 or MotorMaster Euro (Shell) oil, they meet VW and A40 specs. Cars run great while he agreed to lower OCIs to 10K km from 15K km he used before me.