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That sounds strange. You can try to clear data for camera under settings > apps > all > camera > clear data. Restart your phone and try again.
If you still experience the camera slow I would suggest that you start your phone in safe mode:
I would suggest that you try to boot your phone into safe mode to see if the problem may be related to any 3rd party app that you have installed in your phone:
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008#U348008
