Your iOS 5.01 has 2 portions:
1) the actual OS running your apps and such
2) The baseband; the radio portion.
5.01 can be jailbroken, the BaseBand that comes with 5.01 cannot be unlocked.
What you can do is update your phone with the OS portion only, making a custom firmware version without the BB.
You can do that with the jailbreak tool redsn0w.
After updating with this custom firmware, you will have the 5.01 OS with your old BB which you can than unlock with Gevey sim using an app called furious mod.
Better start reading up on this forum and on iclarified.com
You can mess-up your phone if you don't do it correctly.