Nope u can't. U need absinthe (a program for Mac/Pc in order to jailbreak it. The instruction I used was from [Moderator edit: Removed link to another site. We have a very nice tutorial on how to jail break with Absinthe in the Hacking section of this forum. Please use that. Thanks.] The process takes about 5-10 mins.
If you mean directly on the device itself, no. There's no JailbreakMe-like jailbreak for 5.0.1. You'll need to use GreenPois0n's Absinthe via a computer to do so.