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The Radeon 5770 is one of ATI's newest video cards. Its performance is roughly on a par with the Radeon 4870, which is to say it is quite fast and is more than capable of meeting the needs of most gamers.
However, the Radeon 5770 has new features which the Radeon 4870 does not. It supports DirectX 11, while the Radeon 4870 only supports DirectX 10. The Radeon 5770 also supports Eyefinity, a multi-monitor gaming and productivity feature. The Radeon 5770 also tends to run a bit cooler and quieter than the Radeon 4870.
Of course, those extra features don't come free, so the Radeon 5770 retails around $165 dollars, fifteen more then the Radeon 4870. It is arguable if the features are worth the extra money, but it is nice to have the choice.