I do not have enough free space on the C:\ drive of my Windows computer to run the updater for iOS 5 in iTunes
I think that iTunes is trying to use your gobal Windows temporary folder. By default, this directory is in your user Local Settings directory, located on the same drive as Windows. This is a system-wide setting that applications are supposed to follow.

You can change the path to this temporary folder by changing the value of the TEMP environment variable. You'll have to restart iTunes after changing the variable to have it take effect.