It is not some crappy PSU that came with a $20 case. It's a Dell Studio 540.
Perhaps you should read closer. The OP stated his computer has a GTS 240. That card is the OEM version on the 9800GT, not even the newer version without the power connector but the older more power hungry version. You can read about it here;
http://www.nvidia.com/object/product_geforce_gts_240_us.html
That card uses slightly MORE power than a HD5770, as I already stated. There is absolutely no reason in the world to think his computer can't handle a card that uses less power than his current one.