There is a way but it's not convenient, you have to take a photo while your recording a video for it to be full screen. The iPhone 5 display is 16:9 while the camera is 4:3.
Use an app like ProCam for full-res 16:9 or 3:2 photos.
If you shoot a still whilst recording a video, the resolution is much reduced at only 1920x1080
I have tried shooting with procam and full screen in 16.9 comes when you rotate phone to landscape. Am I doing it right?