There are two ways to get an untethered iOS 5.0.1 jailbreak. If you’re already jailbroken (tethered), you need to use Corona Untether 5.0.1. But, if you’re still running the stock iOS 5.0.1 firmware on your device, then you need to follow this tutorial. If you are looking for an unlock, follow this guide which will show you how to preserve your baseband for an unlock.
Plug your device into the computer and put it into DFU mode
Open RedSn0w and click “Jailbreak” and a few seconds later, select “Install Cydia”
That’s it! You now have an untethered jailbreak on your 5.0.1 device. If you have any question or issues, leave a comment and I will do my best to reply with a solution.