6670 is not a rebrand.
from the best gaming gfx cards for money articlehttp://www.tomshardware.com/reviews/gaming-graphics-card-review,3107-2.html
Although it's true that the Radeon HD 6670 DDR3 has a more capable GPU featuring a 25 MHz-faster core clock, four more texture units, and 80 additional shader cores, the 5670 wields more than two times the memory bandwidth thanks to its 1 GHz GDDR5 subsystem.
if you can afford, get a 7750 for yourself and give the 5670 to your mother's pc provided that the 5670 meets her needs.
Thank you, I should have read that more closely. I have ordered a Sapphire 1 GB 7750 from NewEgg.
The part that confused me was this:
The Radeon HD 5770 (also available re-badged as the Radeon HD 6770)
I saw that, and my temporary dyslexia read it as a 5670.
Once again, thanks.