There's not much wrong with an i7!
The biggest holdup is the HD5770-I assume you're playing at 1080 rez BTW.
A HD7950 would be a good upgrade, as would a GTX760, their performance is nearly identical with the 760 being a little quicker overall but the 7950 usually comes bundled with some AAA games.
Check the installed power supply can run a new card, it'll need at least 500Watts and dual 6 pin PCI-E leads to run either of those cards, with some 7950s needing 1x6 and 1x8 pin connectors. The card should come with at least one 6-to-8 pin converter. Do NOT use molex/PCI-E converters, if the PSU does not have enough PCI-E leads you'll need to get a replacement.
Not all 7950s are equal, avoid those with a single cooling fan, they are often 'cheap' but pay for it by being hot and noisy under load. All the major makers have superior cooling solutions in their product lineup with the Sapphire VapourX cards considered amongst the best.