I got an intel i5 processor with a gtx 660 graphics card. Can I run battlefield 4? If so, how well?

Minecraft and Team Fortress should run at maximum settings at 60 fps but battlefield may run extra settings at 20 fps so you may have to run at high or medium settings but the game still looks amazing like that.

Yes you can run it the minimum requirement of bf4 is only 512 Mb of Vram and dual core processor