Battery Issues on iPhone 5, ergo, restoring current phone to a 'new' phone.

I have a problem regarding the battery-draining issues on my iPhone 5, so I decided that I should restore/register or whatever you call it as a 'New iPhone' (using the same phone, of course), but I don't want to lose my contacts and messages along the way. Is there a way to do that?

Or is there a way to fix the battery draining problems I am currently experiencing on my iPhone 5? I have tried to 'Reset All Settings,' but I guess, it did not work. Thanks!

Btw, my phone was 6.1.4 a week ago, experiencing the same problems and now, it's currently on iOS 7 (beta 3), and it's still experiencing the same problem.