You can try running it with your current power supply. The worst that might happen is you're computer won't turn on properly. If that happens, you can easily replace it. Try a 500W power supply with a decent +12V rail. I can't remember what are the guidelines to buying a psu, but I think it should be around 30amps or more.
BTW the 4850 is definitely a good idea. Best bang for the buck anywhere near $100.
Interestingly enough, I used to have a 6150 until I upgraded, and my current specs are nearly identical to yours, and it is more powerful than I need.
DX11 is nice but on your budget you should be getting the best card you can for the money. The HD4850 is approximately 35% faster than the HD5670 at your resolution.
If you would like the DX11 equivalent of the HD4850 it is the HD5750 but you will have to spend more; http://www.newegg.com/Product/ProductList.aspx?Submit=E...