It means five feet and zero inches. We don't know the context, but it is possible that the subject's height is being compared to someone else's who is taller, or maybe the writer simply wants to emphasize the point that the subject of the sentence is short. It could be slightly disparaging.

"Nothing" means "zero" here, so five feet and zero inches. For example, you might be able to say "He's five foot zero" to mean "five feet and zero inches", but I don't think it's very common. You'd probably hear "five foot exact(ly)" or some other phrase. But you'd more often hear it in something like "He's five foot ten" if he were five feet and ten inches tall, for example. Of course this is if using the imperial system instead of the metric system. It's hard to give other examples off the top of my head, since to me this is a rather casual use of "nothing".