My New car says it takes 5w-20 and I just accidentally put 5w-30 in my car... now I'm worried.

I heard that 5w-0 is used in the winter because it has a lower viscosity which allows the fluid to move easier in the winter, and 5w-20 is used in the summer because the ambient temperature loosens up the viscosity?

What does the 5w stand for and if my car says to use 5w-20, is it safe to use 5w-0 in the winter and 5w-30 in the summer 

I just dont want to damage anything.