Will this pc be able to run next generation games for the ps4 in 2014

wait and see.
in 2014 AMD HD 9000 series will likely be out or Nvidia 800 series. lol

I'll let you know as soon as they deliver my new time machine  

dude..i don't think anyone can tell you that for sure..maybe or maybe not

its unlikely that a dual core will be able to run console prts when the new gen arrives. gfx wise most of us will be ok as long as you have a dx11 capable card. in a 550ti or better. but cpu wise its likely you will need a minimum of a quad core as the new gen is promising more threading.
not only that console ports are notorious for being badly ported back to pc... the tradgedy is that there written on pc, ported to console then ported back to pc... i dont know why they dnt just give us the pre console port versions of games. im pretty sure they would run much better.

I doubt any of the GTX500 series will be on par with the next gen (2013) consoles once they come out.

- Maybe the GTX580 will be.

- Sure, they'll all probably also be using sub 2 billion transistor GPU's, just remember that the GTX560 and GTX400 series were not all that different.

- Even though the GTX560 does have ~ 1.95 billion transistors it's not as efficient as the more recent tech.

- Honestly between the ~ GTX260 and GTX560 there were not a huge number of performance breakthrough features. As in significantly increased performance per transistor.

- The consoles will integrate either of, or perhaps both, eDRAM and/or XDR-RAM alongside the GPU so it's performance will be 'better' than some of the initial 'on paper' specifications indicate. (Later on more up-to-date specifications of the hardware within the consoles will be made available --- this is pretty much the norm).


The GTX600 series brings far more enhancements to the table, as does/did the Radeon HD7000 series.


PS: The Core i5 desktop processor is a quad-core processor.
- http://ark.intel.com/products/65511
- You have very little to be concerned about regarding your CPU, except perhaps that you are under-clocking it by 100 MHz

thing is the console has been slated to be running an ati card again with the 7670 or 7770 being the general consensus for price to power. microsoft are not willing to sell there console at a huge loss this time they are trying to get it down to less than 50$ loss per unit at launch instead of the 300 per unit at launch for the 360. so thinking there will be a 300$+ gfx card in em is unrealistic.
the next gen will be abit more powerful in real terms than the current 1 other than the dx11 improvements they are also sticking to the 30 fps limit.