iPhone 5, Lightning connector don't list video-out support, promote AirPlay and an Apple TV instead
Apple's old 30-pin iPod connector carried a lot of legacy support through the years, but it also was a capable, if chunky, connection. Those 30 pins could handle a whole hell of a lot, including serial, line-in, and component and composite video. With the switch to the new 8-pin Lightning connector on the iPhone 5, new iPod Nano, and new iPod Touch, some notable benefits were achieved, including a full digital pipe, a fully-reversible design, and a much smaller footprint. But some things might have been lost, like video out.
For the iPhone 4S, Apple's tech specs lists under TV and Video that the smartphone supports AirPlay streaming to an Apple TV, 1080p mirroring and video out over the Apple Digital AV Adapter (Apple's 30-pin-to-HDMI joiner), 480p/576p with the Apple Component AV Cable (RGB plus stereo audio, since discontinued in favor of the HDMI adapter), and 480i/576i with the Apple Composite AV Cable (yellow video, stereo audio).
For the iPhone 5, there's AirPlay. You can stream 1080p video to a third generation Apple TV (which supports 1080p) or 720p video to the second generation little black box (which doesn't support 1080p), and you can mirror your iPhone 5 to either black streaming box at 720p. For what it's worth, 720p at 720x1280 pixels is close to the iPhone 5's turned-sideways screen resolution of 1136x640. Either way it would have to be scaled up to 1080p, so broadcasting the mirroring at 720p offloads that upscaling processing to the external display instead of the iPhone, saving precious battery life, preserving Wi-Fi bandwidth, and keeping that A6 processor a bit cooler.
In case you're wondering if you might be able to get video out working on a soon-to-be-yours iPhone 5 with the Lightning-to-30-pin adapter or cable, don't hold your breath. Both adapters state video out functionality is not supported.
There are two possibilities here. Either physical video out has gone the way of the floppy with the Lightning connector, or Apple will at some point make break-out cables that translate the Lightning digital signal into HDMI, VGA, and older formats.
If hard line video out is gone, in a way it makes sense. Apple's charging forward with wireless streaming, but it's frustrating for anybody who regularly uses the adapter to display what's on your device on a bigger display without the need for a wireless network. Any presentation-giving road warrior that got used to just plugging their iPhone or iPad into a projector or HDTV via an adapter in the boardroom they're visiting will be facing a future of carrying around an Apple TV, HDMI cable, and an Airport Express just to get video off an iPhone 5 (and presumably future iPads) and onto that bigger screen.
If Apple is planning to release breakout cables, like they have for Thunderbolt on the Mac, let's hope they do it soon. Let's also hope Apple's planning to license AirPlay video streaming to display and projector manufacturers, and including Wi-Fi Direct coupling capability so one can hook up to them without a wireless network present. If not, the Lightning connector just made mobile presentation life a lot more difficult.