Since Apple has introduced an APTicket/APNonce check for restores to iOS 5, the TinyUmbrella TSS Server procedure does not work anymore when restoring to any version of iOS 5 that is not the very latest iOS version. Instead, you need to create and restore to a Custom IPSW with stitched blobs. (You can only use this process on A4 or earlier devices such as the iPhone 4 or earlier; you cannot use this process on A5 or later devices such as the iPad 2 or iPhone 4S.)
To successfully restore to iOS 5.0.1, you must have iOS 5.0.1 SHSH blobs saved for this device in your computer (what are SHSH blobs and why are they necessary?). If your device was previously jailbroken, Cydia may have been able to automatically save iOS 5.0.1 SHSH blobs for your device. You can try retrieving SHSH from Cydia's servers by runningTinyUmbrella, plugging your device into your computer, clicking the "Advanced" tab, checking "Request SHSH from Cydia", noting where the SHSH will be saved in "Save SHSH Folder", unchecking "Set Host File to Cydia on Exit", and then clicking "Save SHSH" at top right. Verify that your 5.0.1 SHSH blobs are saved (in the General tab) and close TinyUmbrella before proceeding.
Once you have 5.0.1 SHSH saved in your computer, follow these steps to stitch a "Custom IPSW with blobs" using redsn0w (compatible with Mac and Windows):
Open the latest version of redsn0w (available from the Dev Team Blog).
If your device is an iPhone, first create a NO_BB custom IPSW using redsn0w and then follow the rest of these steps. (To do this, open redsn0w, click "Extras", and click "Custom IPSW".) If your device is an iPad or iPod touch, ignore this step.
Click "SHSH blobs" and then click "Stitch".
Locate the IPSW for the version of iOS you want to downgrade or upgrade to. If your device is an iPhone, select the NO_BB custom IPSW you made earlier. (You can also make a custom IPSW using sn0wbreeze if you prefer; see below for links.) If your device is an iPad or iPod touch, you can use a stock IPSW from Apple; this may be already on your computer.
Click "Local" and select the saved 5.0.1 SHSH blob you saved in your computer earlier.
redsn0w will now begin creating your signed IPSW. It will be saved in the same location the stock IPSW was located.
Enter Pwned DFU mode with redsn0w or iREB. (In redsn0w, go back to the Extras menu and click "Pwned DFU".)
Open iTunes and hold down the "Shift" key (on Windows) or "Option" key (on Mac) and click on Restore.
Navigate to your iOS 5.0.1 signed custom IPSW and select it.
The rest will be a normal restore process. You should now have successfully restored your device to iOS 5.0.1.
If you use Windows, an alternative to redsn0w is to use sn0wbreeze 2.9.3 in iFaith mode to create a custom IPSW with stitched blobs (which can also be useful for people who need to preserve an unlockable baseband since sn0wbreeze custom IPSWs always avoid baseband updates). sn0wbreeze is available to download here, along with the stand-alone tool iFaith that can stitch blobs: http://ih8sn0w.com/
You may also pull partial 5.0.1 SHSH blobs from your device if it is currently on 5.0.1, using redsn0w's "Fetch" function or using iFaith.
If you get any iTunes errors while restoring, check this list of error solutions for some ideas on what might have gone wrong. If you're using the redsn0w process and you get iTunes error 1, try going through the process again but make sure to include the step of making a custom firmware that preserves your device's baseband - or try using sn0wbreeze/iFaith instead, which will also preserve your device's baseband.