Can I run XFX Radeon HD 5670?

Yes a 400W power supply is enough to run a single Radeon HD 5670.
If you are running 2 Radeon HD 5670's in CrossFireX, you will need a 500W power supply.
 
I have another question. Can I run it on this motherboard - http://www.gigabyte.bg/products/page/mb/ga-945gcm-s2c/
I ask, because the videocard is GDDR5 and I'm not sure that my motherboard supports it.
You will be fine, dedicated graphical memory is only dependent on the card itself not the motherboard.

All you need is a motherboard that supports a PCIe x16 card slot, power to run the card, and of course proper drivers.
 
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