Don't feel too bad about your performance, I got pretty high usage with my i5 3570k too in BF4 multiplayer, that game was a mess on pc tbh. I even overclocked it to 4.2ghz and it didn't help much. My hd 7950 always had bad fps dips, but when I used my stock i5 3570k, with an xfx hd 7870ghz, on 64player gulmon railway conquest 1080p ultra (no msaa) it stayed at 60fps constant basically. Multiplayer can be hard to benchmark and BF4 has been buggy as hell since its launch, I've scoured here and on battle log in the many months since the game's launch, and even people with i7s and sli gtx 780s were having bad fps dips. Ever since a july 8th patch last year iirc, BF4 performance was crippled for many people.
I do agree with you guys in this topic though, so many people here will just say a cookie cutter response of a low clocked locked i5 and claim it'll run anything demanding perfectly fine, the person above was right, overclocking is there for a reason when something is really cpu demanding so performance wouldn't suffer.
You should be getting MUCH better FPS with a gtx 970, it's overkill for 1080p gaming. I don't remember the forum topic off hand from battlelog, but a guy was having bad fps with an r9 290 and he upgraded to a gtx 970 and it fixed all his problems, and I think he said he got..maybe... ~100fps. Don't quote me on that, but it was a high number and it's been months ago, but it was certainly better than 60
with the performance you're wanting, you're going to want an overclocked i7 tbh, that's the top CPU for gaming, and with the consoles using 8 core cpu and many new games recommending an i7 cpu, if you really want the best I'd go i7 for the 8 threads. I honestly see i5s getting more and more bogged down as time goes on, due to sloppy console ports. It's sad we as pc gamers have to do this. Myself personally, I'm not going to spend the money on that, and either I wait for benchmarks to see how games perform on my hardware, or I'll get bad ports on console to avoid the headache. I've had nothing but problems out of BF4 on pc. But you know what? Even though it has obviously worse graphics, the old Xbox 360 version was more fun to me.
in short, BF4 and GTA 5 aren't exactly the best pc ports tbh, and others with stronger PC's even have issues. If my hd 7870ghz could match your gtx 970s fps, something is definitely wrong.