Sorry to be the bearer of bad news but it has been confirmed for now that there will be no untethered iOS 5.0.1 jailbreak, so you're advised to not update your iPhone, iPad or iPod touch to iOS 5.0.1 firmware when it becomes available for public.
Well known hacker of the Chronic Dev Team @p0d2g made this heartbreaking revelation through his twitter account. Recently, a bug was discovered that led to an exploit capitalizing on which an untethered iOS 5.0.1 jailbreak could be developed and released later on. However now it has been confirmed that Apple will patch that bug and close the exploit before it releases iOS 5.0.1 firmware to the public for supported iPhone, iPad and iPod touch.
The bug in question here was initially found by Charlie Miller. Basically, this bug would allowed for an early untethered iOS 5.0.1 jailbreak release but since Apple is going to patch this bug in their next firmware update, its back to square one for jailbreak developers. Do keep in mind that @p0d2g's bug and Charlie Miller's bug are separate. What this means is that there will definitely be a way to jailbreak iOS 5.0.1 untethered, but it will take a lot more time to be released.
Back in September the Chronic Dev Team revealed that they had five new exploits that could be used for untethered iOS 5 firmware jailbreak. It is not yet known whether Apple has patched the said bugs in iOS 5 or the upcoming iOS 5.0.1 firmware, however it can be said for sure that even if it takes a lot more time than it should, sooner or later there will be a way to get untethered iOS 5.0.1 jailbreak on iPhone, iPad and iPod touch.
Currently the only way to jailbreak iOS 5 or iOS 5.0.1 firmware is to settle with a tethered jailbreak, one that requires you to connect your device to the computer every time it reboots. The full instructions on how to jailbreak iOS 5 firmware can be found here. On the other hand, there is also a way to get an iOS 5 untethered jailbreak of sorts using a Cydia package that is installed after the initial tethered jailbreak has been applied. To get an iOS 5 untethered jailbreak of sorts, follow the detailed instructions posted here.
iOS 5.0.1 has currently been seeded only to developers, though you can download iOS 5.0.1 beta 2 for your device from the links we've posted. This firmware update will not come with any new features, only bug fixes and overall performance improvements. iOS 5.0.1 firmware is expected to be released in the next couple of weeks.