Al parecer Apple no incluyo la funcionalidad en el conector nuevo Lightning para poder sacar video desde el iPhone según indica la pagina de las especificaciones. Sin embargo el iPhone 4S que utiliza el antiguo conector si tiene esta capacidad.
Chequea la lista;
iPhone 5: TV and Video
● AirPlay Mirroring to Apple TV support at 720p
● AirPlay video streaming to Apple TV (3rd generation) at up to 1080p and Apple TV (2nd generation) at up to 720piPhone 4S: TV and Video
● AirPlay Mirroring to Apple TV support at 720p
● AirPlay video streaming to Apple TV (3rd generation) at up to 1080p and Apple TV (2nd generation) at up to 720p
● Video mirroring and video out support: Up to 1080p with Apple Digital AV Adapter or Apple VGA Adapter (adapters sold separately)
● Video out support at 576p and 480p with Apple Component AV Cable; 576i and 480i with Apple Composite AV Cable (cables sold separately)
Posiblemente veremos a Apple sacando un adaptador de Lightning a HDMI para lograr sacar video. Por el momento todos nos vamos a tener que conformar con el Airplay Mirroring del Apple TV.