I contacted AMD and this was their reply:
Your motherboard is a G31 Intel chipset. From what I can see online it is a PCI Express 1.1 compliant motherboard.
The HD5xxx series cards are PCI Express 2.1 hardware compliant, they are backwards compatible to PCI Express 1.1a motherboards but have issues with earlier revisions. Issues range from no POST to simple wake from sleep issues but can also include instability, poor performance and graphics corruption.
Check with Gigabyte for any BIOS updates and see if they recommend PCI Express 2.1 cards in this motherboard, you are right at the borderline of compatibility.
The safest recomendation would be to stay away from HD5xxx and higher cards, the HD4xxx series is safe to upgrade to.
In order to update this service request, please respond, leaving the service request reference intact.
Best regards,
AMD Global Customer Care
Then i contacted Gigabyte and their reply:
Thank you for your kindly mail and inquiry. The card is PCI-E rev2.0 which is compatible with PCI-E 1.0 slot.
If you still have any further question or suggestion about our products/service, please do not hesitate to contact us. We will try our best to help you resolve the problem ASAP.
Regards,
GIGABYTE