Does the Lightning to 30-pin iPhone 5 adapter support video out?

No, Apple's Lightning to 30-pin adapter does not support video. The adapter will support audio out, syncing and charging only.

Future Lightning cables are in the works and will support video. Apple plans to release iPhone 5 Lightning to HDMI and Lightning to VGA video cables as separate accessories.

Apple launched the Lightning reversible 8-pin connector to replace the 30-pin dock connector that has been in use on their mobile devices since 2003.