If your PSU is of decent quality, it will support a graphics card as strong as a GTX670 or 7950.
A GTX670 is a $400 card, but I might suggest that a GTX660 @$230 or so would be a significant boost in graphics capability that would meet your major objective of running at high settings.
Similarly, a 7850 0r 7950 if you prefer amd.
You might be concerned about the ability of your older E5400 to cope.
Most games do not make good use of more than 2 cores, so you may be ok.
To help clarify your options, run these two tests:
a) Run your games, but lower your resolution and eye candy.
If your FPS increases, it indicates that your cpu is strong enough to drive a better graphics configuration.
If your FPS stays the same, you are likely cpu limited.
b) Limit your cpu, either by reducing the OC, or, in windows power management, limit the maximum cpu% to something like 50%.
This will simulate what a lack of cpu power will do.
Go to control panel/power options/change plan settings/change advanced power settings/processor power management/maximum processor state/
set to 50% and see how you do.
If your FPS drops significantly, it is an indicator that your cpu is the limiting factor, and a cpu upgrade is in order.
It is possible that both tests are positive, indicating that you have a well balanced system, and both cpu and gpu need to be upgraded to get better gaming FPS.
If you decide you want to upgrade the cpu, you are looking at new ram and motherboard as well.
A ivy bridge cpu is likely the best way to go. A i3-3220 is about $130, or a i5 quad is $200. A Z77 motherboard will be <$100, and since ram is cheap, I would suggest a 8gb kit for about $45. If you current copy of windows is oem, you might need a new os too.