I have a '12 Enclave and I would avoid a trailer that heavy. I would look for one with a GVWR near 4k at the most. The links below are for an Enclave forum. The suspensions differs between the Buick and the Chev/GMC cousins (reason for the lower towing cap on the Buick), but they do have the same drivetrain.
Here are a few links to threads about towing with the Lambda models. Notice the weights they are carrying, and what their engine temps are doing.
http://www.enclaveforum.net/index.php?topic=7343.0http://www.enclaveforum.net/index.php?topic=8951.0http://www.enclaveforum.net/index.php?topic=4991.0