Who said 1080p. It is 2560x1440.
You described it yourself as 2K. If you meant 2.5K, you should have said so. That's a game changer. 2.5 is not a mere 25% more pixels, it's a whopping 78% more. Literally 3,686,400 pixels, vs 2,073,600 pixels. It's quite a difference really, and something you should have clarified from the get go instead of calling it 2K. I don't recall you mentioning the display's refresh either, which of course matters a lot.
And of course most games are going to be unplayable at that res with a 5870. Are you beginning to see what I mean by clinging too long?
Back to the new GPU though, while a 980 or 390X
would be more suited to 2560x1440 than a 970, you'll be spending about $200 more and only needing the extra power in a handful of the most demanding games, and that's only IF you insist on max settings in all games, which often isn't needed for decent image quality. Depending on preferences, some settings can even degrade image quality. Come time for Pascal's launch though, we'll then see if you think you spent that added $200 wisely.
A 1-1.5 yr old 970 come launch of Pascal would still have fairly good resale value, especially considering the performance enhancements that Dx12 and CUDA 6 (uni mem) will bring once 2016 games debut. So what I'm saying is this future proofing is not going to be very long lived given the tech that's coming, so best buy in affordably and resell it if you're going to buy in now, particularly since you like to keep your GPUs so long. That mindset only comes close to working if you get a GPU that has huge advances in tech, which Pascal will.
My bet is that you would lose only half of that extra $200 you would have spent on a 980 or 390X, reselling the 970, and end up getting much better tech going forward beyond 2016. Sure you'd be out $100 or so, but not really, because that is time spent using a pretty good GPU. You'd probably take that suggestion more seriously were you not hung up on the VRAM thing needlessly.
It really comes down to what you can afford and/or how much you want to spend, but regardless, clinging to a GPU for too long will only get you back to where you are now, with a card that can't handle any game you throw at it. Most gamers would never put themselves in a situation where they're waiting to decide on a GPU, while having lots of high end gear, yet a GPU not good enough for any current games.
With more games popping up with supersampling and now with AMD and nVidia drivers allowing higher than monitor default resolution even a 290X and 980 can to slow even more so when you add MSAA or a like..
Then again, with 78% more pixels, you don't really need as much AA. That's a LOT of pixels for a 27" screen. It comes out to .2335 mm pixel pitch, which is way tighter than you need even for ultra sharp text, let alone AA.
For comparison sake, the first 2560 displays that were said to be the first ultra tight pitch large displays (30" 2560x1600), were only .2524 mm pitch, and even they were touted as requiring less AA.
http://thirdculture.com/joel/shumi/computer/hardware/ppicalc.html