Well the AMD and I3 are both dual-core processors. The i5 is a quad core and therefor will be much better for gaming, that is if the games you are playing actually utilize all 4 cores. Some games only use 1 or 2. Mind providing some more info on the laptops you are looking into? Without a dedicated graphics card, gaming could be pretty laggy or unplayable.
Laptop i5 are dual core, only laptop i7 with a "q" are quad core. You'll need to be more specific to get a better answer. You could even just give a budget for the laptop and we could give some suggestions. You'll also want to say what you will be using it for.