While using my camera, it turns off without my doing.

Camera battery pack is inserted into charger and charger is plugged into wall, however the battery pack is not charging.

Hello Edwin, You may have been moving the camera while taking the picture. Even slight motion will cause the image to be blurry so make sure the camera readjusts itself before snapping a picture. I also advise wiping the camera lens with a proper cleanser to fully solve this issue. The device page for the Sony Cybershot dsc-t5 can be found at Sony Cyber-shot DSC-T5.