No a 1220 will not help. It is a 4 core 4 thread cpu just like your i5 is.
Plus it will not actualy fit in your motherboard it is s socket 1150 and yours is an 1155.
In games like BF1 that can use more then 4 threads an 8 thread Xeon like the e3-1226 would help but again that is also a haswell socket 1150 cpu.
Only improvments you have as an option are socket 1155 i7 cpus (so 2xxx and 3xxx model numbers) and those are going to cost some money.
Oh, cheers for the reply. I thought it was a socket 1155 cpu, my bad. Guess I'll just stick to my i5 and wait it out. Thanks