I tried it in the x1 slot, x8 slot, and the x16 slot and get the same thing. I have two other cards for testing, a 3450 and a 7850. Shortly after my last post, I orderd a x8 to x16 PCI slot adapter from Orbit Micro, so I used that to try my old 3450 in one of the x8 slots and it also worked fine. The 7850 has no issues either.
I'm thinking either it's a problem with this particular card HIS HD 5450 x1, or the card in combination with my Asus Z8NA-D6C motherboard. I'm going to try it with a different motherboard, an ASRock Z77E-ITX. If that doesn't work, I'm going to try to return the card.
Searching through earlier posts in this thread, I get conflicting reports with the 5450 so I'm guessing it's possible it's the card.