Before running the latest untethered jailbreak from both the Dev-teams, you should know some facts about the jailbreaks, which can help you have a silky jailbreaking experience.
1) The latest jailbreaks, Corona 5.0.1 Untethered and Redsn0w 9.10b1, work on iOS 5.0.1. So update your devices to iOS 5.0.1 if you are still stuck with iOS 5.0.
2) This untethered jailbreak will work only if the device is powered by A4 processor. iPhone 4, iPhone 3GS, iPad, iPod Touch 4G and iPod Touch 3G are the devices which can be jailbroken with Corona or Redsn0w 9.10b1. This jailbreak will not work on A5 devices like iPad 2 and iPhone 4S because a bootrom-level exploit is yet to be discovered by any of the hackers.
3) If you have an already tethered jailbroken A4 device, then you do not have to go for iPhone Dev-team member MuscleNerd's Redsn0w 9.10b1. All you need to do is just go to Cydia in your jailbroken device, search for the jailbreak released by the Chronic Dev-team's French member, Pod2g, by typing Corona.
Once you find Corona, download it and run it after installing and your device is untethered jailbroken now.
4) If you are jailbreaking your device for the first time, then you need not to go for a tethered one. You can directly download Redsn0w 9.10b1 and run it in your device to jailbreak it. Redsn0w 9.10b1 has Corona packaged inside, so you don't have to go for two different procedures to get the untethered jailbreak.
5) There are many reports of the jailbreaking going wrong and if you are not familiar with jailbreaking, then we advise you to back-up all your data before going for the jailbreak. It saves your valuable data in case the jailbreaking goes wrong and your device needs a restore.