Sure, but if you are going to bother upgrading that isn't the card I would suggest. Tell us more about your computer, monitor's resolution and budget and we can probably suggest some better choices.
Or do you have a better suggestion as to where to purchase a decent desktop for casual gamer. I was advised to get at least 450psu with either gt240 or hd5670. I've been driving myself crazy trying to configure these things and I do not know much about computers...although I'm beginning to learn.
If it is a Dell they actually use decent PSUs and rate then for continuous usage rather than peak like most manufacturers. That means their 350w is more like a 400w+ by normal standards. You can use an HD5670 on that PSU but you can also use more powerful cards like the HD5750 or HD4770.