I had the same problem. I could not reduce the screen brightness on my iphone 5. I knew it was a hardware problem because it happened after i changed my battery. i opened my phone while it was on and the brightness reduced but it would jump to full when ever i tried to close it. while it was opened i noticed the screen's brightness would jump to full whenever i press the shield on the display connectors. i loosened the screws and closed my phone which fixed the problem. I think its a grounding issue or something like that.
When i squeeze the top right corner really hard the brightness increases to full but other than that its ok.