That card is leagues better than the 780G. Just for comparison, the 5570 has ten times as many stream processors. You should be able to play any game out on at least mid settings, most older games on high. You should be able to find a better price, though. Personally, I love newegg.com, and I just checked and they have 5670s, which are better, for cheaper.
I agree with what Jryan388 said one thing to keep in mind however is if your PSU can handle the new card (HP's have had some very under powered power supplies in the past). What is the wattage of the psu you have in you pc right now?