A 5 minute game is precisely that. Each side gets 5 minutes for the entire game. If one side runs out of time, they lose providing the other side has mating material. If not then the game is a draw.
15/5 means 15 minutes per side with a 5 second increment.
I hate to be stupid, but I don't understand the timing rules in games against other people online. Like if it says "5 minutes" well... what does that mean? Who wins after five minutes? or what? And the ones that say something like 15/5, well shit, what is that?? sigh