That's a FSP PSU. According to its label, the +12V rails are actually additive (usually they aren't), which means it has 23A. You will have no problem with a HD5670. If you're just looking for the strongest card you can run without a PCIE power connector, get a HD7750.
AMD specifies a 400W PSU for that card in an attempt (often vain) to compensate for all the cheap PSU-shaped objects out there that aren't actually good for what's on their labels.