Interesting thought experiment, though I do agree that having such a sum comes with the pressure to be a responsible steward - both internally, for one's own conscience, and externally, since people know you have the money. It's a problem I'd be willing to take on, though ;)
First I think I'd figure out exactly how much money I needed to never have to worry about money again, and then I'd double or triple that just to be safe - which wouldn't even scratch the surface of this $5B. I'd buy the 2-3 houses I want (which should, all 3, barely crack $1M...maybe $1.5M). I'd work part-time, maybe 20 hours a week. I'd make sure my family (especially older family) got the very best healthcare imaginable. I'd knock out some debt for those closest to me. I'd give myself a monthly allowance to buy all the small things I want on a regular basis - steak, fish, $30 tubes of makeup, etc. I would probably go back to school at some point, since I miss that environment. I'd go on mission trips. I'd travel a lot more.
And then....the possibilities are endless. I'd spend a lot of time thinking deeply about what I really care most about and developing a strategy to donate, set up funds, etc. for those causes. Stewarding that money and overseeing its uses, ROI, etc. would probably be a part-time job's worth of work.
I might buy something - a grocery store, a sports team, something of the kind - but I'm not sure. I don't have any desire for really nice cars, big houses in HCOL areas, etc...but maybe I'd feel differently if those purchases were within my financial means?