There are a few things you can do to test what the problem is.
I presume you have not overclocked the FX 8320 AMD cpu in anyway.
The first thing is to go into your bios.
Have a quick look at what the bios is reporting the cpu temperature at in celsius, 36 c to 40 is fine if you are using the stock cpu cooler that came with the FX cpu.
Ok turn off the option of AMD cool and quiet in the bios.
Turn off the option of power saving mode for the core of the cpu C1E
And any option that states P wait stating. C6
Save the changes made in the bios before you exit it.
Then let the system boot into windows.
Now you need to go to the power options settings in windows.
Open it up, and select the high performance profile and click ok or apply.
If at any point you had the Nvidia GTX 660 card in the system and installed the driver for it.
And then swapped the cards over and put the GTX 560 card in the system.
The problem is the driver you installed.
Click on the link bellow and download and install the program, then run it on your system.
Choose to clean all Nvidia video drivers from the system.
http://www.guru3d.com/files-details/display-driver-uninstaller-download.html
Once done the program should ask you, or reset your system.
Let windows boot up again.
And then head off to the Nvidia website and support section for drivers.
Get the latest driver you can for the model range of GTX card you have fitted to your system the 560 card.
And Install it.
Restart the system once installed.
Let windows boot up again and then test it again by running your game.
Post back just to let us know what the results were, if the frame rate improved in games ok.
NB:The changes you made in the bios relating to the cpu.
Are to prevent the cpu from down clocking in speed in Mhz.
This happens when a low power state mode of the cpu core is signaled by windows.
The P wait state slows down the amount of data able to pass through the cpu. by putting pauses on the clock cycles of the cpu.
Cool and quiet prevents the cpu from down clocking in speed when the temperature tigger set in the bios is reached.