The HD 5570 is a little slow for serious gaming, you should try for a faster card.
A good place to start a search for good cards is the THG article on the best video cards for the money, updated monthly to reflect new prices and new cards. Note that it includes links a very brief description of the performance level of the card plus links to reviews with detailed performance benchmarks, most often with comparisons to other cards:http://www.tomshardware.com/reviews/gaming-performance-radeon-geforce,2997.html
For more general information about how to upgrade video cards, including determining system limits and comparing, selecting and installing video cards, I recommend this site:http://www.upgradevideocards.com/index.html
Also note that on the first page of that web site is a promotional code to get $10 off your first purchase of $50 or more at newegg - should help reduce the cost of a new graphics card. Note that it expires 8/31.
Also, if you are buying a new PC with plans to upgrade the video card, pay careful attention to the size of the PSU as most systems come with a PSU that is only a little larger than what is required for the existing system and, even when the total power is adequate, often don't provide enough power to the 12v leg. Additionally there is a wide range in quality between manufacturers.
For more on power supplies, see:http://www.upgradevideocards.com/criteria.html
Additionally when you think you have identified the system you want, post the information - name of system, PSU wattage, and video card make and model - to this forum and people can help you review it, although it will be difficult to give a definitive response without knowing the model of the power supply which you will likely not be able to get until you buy the system and look inside.