450W GPU with 400W PSU?

Hello.

I recently upgraded my graphics card and I now have my old XFX HD5770 lying around. So my dad asked me if I could install it into his computer if it was possible, fine by me.
Anyway on the box it says that the recommended psu wattage is 450W, however the PSU in my dads computer is 400W.
Can I still install the card into his computer? I've often read that people over-dimension their PSUs and the actual power usage almost never gets to the levels indicated by GPU manufacturers. I mean the PSU even has 2 PCI power connectors and the card only uses one of them. I don't wanna risk breaking anything though.
The full specs of his computer is:

Silver Power SP-400P2C 400W PSU
XFX HD4770
ASUS P5QPL-AM mATX Motherboard
Some Intel Dual Core CPU, not sure which model, thinks its like 2.5GHz or so.
2GB RAM
1 80GB IDE and 1 500GB SATA HDD
1 SATA CD/DVD player
Integrated Audio