The graphics card is a professional class, not a gaming class graphics card. It's designed for professional graphic applications. It and it's drivers are not designed for playing games.
Laptops are notorious for not being upgradeable. Given the difference in generations if the two CPUs you've listed, I would believe, even if the CPU was upgradeable, the new processor would not be compatible with the old processor's CPU socket.
With that processor and that amount of RAM, I would not expect your system to have any issues running any type of office application. I often run an spreadsheet app (LibreOffice Calc) with eight sheets as well as Firefox with between eight and twenty tabs open with no lag on my desktop I5-760 w/ 8GB RAM
It really depends on your usage. 4GB of RAM can be really tight these days and if your regular usage typically needs more than that, it doesn't really matter which CPU you have. If you could get the I5-5220U with 8GB or 16GB of RAM, that's a no-brainer.
Thanks for your reply. Is it a big difference between the processors I mentioned or I wouldn't even feel the difference at all? (I know you said it doesn't really matter but I'd like to know a hypothetical difference)