Are you an avid gamer as well? Or do you not game at all?
If not I think your suggestion is a great one. Even if you are a avid gamer you could give that card to your son and then upgrade to a better card for yourself.
Another option is to purchase a gtx 550 ti or a hd 6850, these can be typically had for roughly 120.00.
Black friday is coming up so your could probably find some good deals on a gpu.
5670 is a good card, in fact it is recommended by tomshardware as the best card under 100.00. The card will meet the demands of your son perfectly fine. http://www.tomshardware.com/reviews/fastest-graphics-card-radeon-geforce,3067-2.html
I have more questions sorry that i forgot to ask.
What is your PSU?
What resolution is your monitor?