The 5670 is an entry level gaming card. It won't max anything out at high resolutions like 1080p. It performs okay at lower resolutions like 720p and 1280x1024. At a lower resolution like 1280x1024 you should be able to pull off high settings on the less demanding games and get about 30FPS. More demanding stuff like Battlefield 3 or Crysis will cause it to struggle much more, with medium settings probably being the best option. If you are at a higher resolution like 1080p, you can do medium on most games, and low for the really demanding stuff.
Be sure to get a version with GDDR5 memory. the GDDR3 version is considerably slower. The 512MB version is fine, as the GPU is not powerful enough to use more than 512MB of RAM, so you don't need to spend extra for the 1GB version.
You may need to upgrade your power supply to run the card. The 5670 is a low powered card, but it won't work with a really low powered PSU, like a 220 Watt unit. You need at least a 300 Watt power supply, 400 Watt if it is a really low quality brand.
