In addition to the problems related to the installation of iOS 5 on an iDevice, some users also complain that the battery autonomy is not so good after installing the new version of the operating system. This is a problem that is discussed after every update to a new version of iOS and in general there are several factors that can cause a decrease in battery autonomy. Among them we find: installing a backup of iOS 4, new functions implemented by Apple that require more resources, excessive use of the device, etc.
Usually the installation of an old backup generates problems of this kind, but you also have to take into account the fact that in iOS 5 there are many new functions that affect the autonomy of the battery, and the most energy-hungry are Notifications Center and iCloud. iCloud updates the information from an iDevice with Apple's servers at certain time intervals and this operation consumes not only internet traffic but also energy and the Notifications Center is so complex that it needs quite a lot of resources to function without problems.
If your autonomy is very bad, I recommend you to do a restore and not to reinstall the old backup, but to set the phone as new. If you have already done this and you are still not satisfied with the autonomy, then check if the GPS/Bluetooth are open, if the Wi-Fi is working when it shouldn't and close certain functions.
