Jailbreaking does not unlock your carrier. There currently isn't an unlock for any version of iOS 5 at the moment. One for 5.0 is suppose to be available soon but will be unavailable on 5.0.1. You won't be able to downgrade to iOS 5.0 anymore because Apple is no longer signing it.
Wirelessly posted (Mozilla/5.0 (iPhone; CPU iPhone OS 5_0_1 like Mac OS X) AppleWebKit/534.46 (KHTML, like Gecko) Version/5.1 Mobile/9A405 Safari/7534.48.3)
Actually, not to argue but it is not known yet if the unlock will work on 5.0.1. It's highly likely that it won't work on the later version(9A406)(revised 5.0.1), but there is a small possibility that it might work on9A405(5.0.1). However if one does come out it is much more likely to be for 5.0.