My battery last 3 maybe 4 hours max ,losses power quick you can just watch the percentage drop it ridiculous !
Thats browsing and a few calls and texts.
I too was getting horrendous battery life on my iPhone 5, and just like you, I had restored my iPhone 5 from an iCloud backup that I had done on my iPhone 4. To fix my battery life problems I "transferred purchases" from my iPhone 5 into iTunes and then did a backup on iTunes. I then fully restored my iPhone 5 and synced all my "transferred purchases" back to my iPhone 5. So essentially I backed up my apps/songs to iTunes, but NOTHING MORE (an iCloud backup backups apps, songs, and other data specific to that device that can screw up the battery life if that backup is restored to another device. Back upping apps to iTunes and doing a full restore with iTunes erases all of that old data that iCloud backup stores and deletes it all.
Now, for most people this would be a bad thing because they'd be losing all of their apps, but this isn't a problem because if you "transferred purchases" from your iPhone to iTunes, your apps will all be there sans the old data from your past iDevice. Now simply sync all of your apps, songs, etc to your iPhone 5, login to your iCloud account to restore contacts, pictures, message threads and other settings and boom you're all done. Your battery life should jump exponentially.
Before I did this, I could only manage 3-4 hours of light usage, with 10-13 hours of standby before it would die. Now I average 6-8 hours of usage with 18-23 hours of standby depending on how I use it. This is a HUGE increase that others can also achieve if they follow these steps.
This whole process took me only an hour to complete (not including the time it took me to download the entire iOS 6 ipsw file). I'd definitely do this if you're getting bad battery life.
Note: I also have LTE and wifi always on, Bluetooth off, auto brightness on, location services always on for many apps, everything on to sync with iCloud, push notifications on for nearly all 75 of my apps, and push email for one email account.
Below are before and after pictures of my battery life before I did this restore and after I did this restore:
BEFORE (LEFT) AND AFTER (RIGHT):
