That's a question I was asking myself the first time I saw such a weird C5 plug. That was a while ago, but I came across it again and haven't found an answer yet.
The only thing I could find out is that C5 is with 2.5A and C13 with 10A. But I guess it would technically be no problem building an AC adapter (e.g. for laptops) in which you plug the far more common C13 connector.