Or will the stock thing that comes with this i5 be ok?
Your stock fan will be fine on a non-overclocked, non-high-end-gaming machine. Especially for Intel. I don't trust AMD stock coolers as much, even just running basic games/programs.
edit: And at first didn't notice you already bought the processor, so most of my suggestions regarding not building a system are probably not relevant. Oh well, for posterity!
For Sims4 and Marvel Heroes I'd almost suggesting finding a private seller offloading an old system or just finding a good deal on a prebuilt. Maybe even a refurbished unit from Newegg or something? Maybe look at some Newegg bundles?
I dunno, building a system for $500 system for a GF to play the Sims doesn't seem cost effective. People build systems to get exactly what they want in a machine, not necessarily to save money or make things easier for themselves.
Why not just get a cheap SSD. If she needs more storage, tell her to stop digital hording! It's also easy to add storage later, even just remotely, so an initial build can survive a single 120/128gb SSD, which will save some money or allow other parts to be improved.
Paying 80 bucks for the OS on $500 system is a budget killer. There are other ways to get legit copies. You don't have an old win7 key laying around from an old system. My secondary build has the key from an old junked laptop that was being thrown away at my last job. Just downloaded the right install files from MS, entered the key, called the automated MS system, tadah. There are people that sell copies too on reddit and shit, but usually someone I know has at least one old key sitting around somewhere.
There are other ways to get a legal Operating System. Can use the key from an old, unused system if you or friends/family have one (the key I'm using on my secondary desktop was originally from a junked old laptop, just have to call MSs automated system to get it re-set.
Any local computer shop? Can often get old cases for next to nothing, and it's something that can be upgraded later if she's not happy with how it looks, or hell, get an old shitty metal case and paint it for her. It's not like you'll need premium air flow or anything.
I'd suggest not getting an optical drive, as it's not that hard to live without these days, but they're cheap and going without can confuse people
