The HD5670 is meant to be a casual gamer card
1) Something that is cheap for ATI to make
2) Cheap enough to be put in OEM boxes such as HP, Gateway, Dell, etc
3) Has thermals (tdp) low enough you can put it in a laptop

The HD5670 has almost the same performance (it is slightly slower) than the performance card of 3 years ago known as the 8800gt/9800gt

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For more performance consider these cards
HD4870 and the HD5770 these cards about twice the performance as your card. The HD4870 generates a little more heat and doesn't have directx 11, but very few games have directx 11 features and no game out there needs directx 11 yet (and there won't be any major game that needs directx 11 anytime soon for the xbox 360 and ps3 are based off older hardware and if they want to port the game to consoles and pc they will require direct x 9)

The HD6850/HD6870 and GTX 460 (even the 768 mb version) is about 3 times faster than your HD5670

The HD4870/HD5770 is the performance card of last year. The HD6850/HD6870 and GTX 460 768 and GTX 460 1024 are the performance cards of this year. How the graphic cards work is there are sorta four main catergories

Functional (barely better than an integrated graphics)
Casual Game
Performance Gamer
Enthusiast Gamer

You almost always get the best bang for your buck if you buy in the performance gamer area. The Enthusiast Gamer has a lot of mark up and the companies make a lot of profit. The Casual Gamer is designed to be good enough to play, but not what you really want to play. The casual gamer cards are where ati and nvidia make there most money for usually they are half the cost to make than the performance gamer parts, have a good mark up, and they sell the cards by the boatloads.

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Sorry I don't have time to write more (or to look for links comparing card x and y), I need to go to work, literally selling the same video cards you been asking about.