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Try resetting your iPhone: press and hold Home and Power button until the Apple logo appears. Release both and let the iPhone power up on it's own. This kind of reset won't remove data or change settings, maybe it'll help with your camera.
If the reset doesn't help, try updating your device. The latest software for the iPhone 5 is 9.1. Before you update your iPhone, make sure there's a recent backup, then connect it to iTunes (computer) to get it up to date.
What you're experiencing might as well be a hardware problem. If that's the case, resetting and restoring won't help. If possible, visit the next Apple Store and let them take a look at your iPhone.