Well, seeing as he's running a 8500GT, which calls for min 18A on the 12v rail as well, so the GT240 should be fine. (I didn't notice the low 12V amperage at first). So yeah, the 5670 requires more 12V Amps than that, so sorry that one won't work (my bad on missing those requirements) but the GT240 has the same requirements as the 8500GT.
Edit: well... my researching gave different results than yours I guess... Maybe MSI has different specs. Maybe what I found was not legit. whatever the case, The newer cards DO seem to draw less power than the 8500GT the OP has, but I guess that doesn't mean it would be a good idea
Thanks for the research Jack and the correction before I let someone blow their PSU sky-high.