When I take a picture it always displays a blurry image.

Hello, This may be a problem with the temperature of the device. If you are in a cold environment or a fairly hot environment this may be causing the problem. To fix this, warm or cool your device down by bringing it to a more appropriate environment, such as a room or warmer or colder area (depending on the situation). This could also be your battery running out of charge. If this is the case, plug the battery into the charger. Device page for the Sony Cyber-Shot DSC-T5: Sony Cyber-shot DSC-T5 Troubleshooting

This may be a case of a faulty charger or a bad outlet. First try plugging the charger into a different outlet. If this doesn't solve the problem it may be the actual charger itself. If this is the case a new charger should be purchased.