mirror iPhone 5 display to TV without AirPlay
At the moment, this is currently not possible as existing adapters are not compatible with the Lightning connector (even with current converters). See this link for more information.

At the Apple event on the 23rd October, two new adapters were announced VGA to Lightning and Lightning Digital AV (HDMI). If you read the details on the store page carefully, they both say they support mirroring (in the overview section).