For a run that long, I would go with the RapidRun from ImpactAcoustics (also available from Parts Express). They have custom length HDMI cables with either a wall plate or flying lead (regular end). The trick is that they have active and passive ends. For a long run, you would have one passive end at the projector and get the active end to put by the source. This is, in effect, a signal amplifier that allows the signal to maintain strength over long runs. They recommend it for runs over 30'.
Cable:
http://www.partsexpress.com/pe/showd...number=183-743
Passive end (flying lead):
http://www.partsexpress.com/pe/showd...number=183-745
Active end (wall plate):
http://www.partsexpress.com/pe/showd...number=183-755
$250 is pricey, I know -- but it's in-wall rated, good to 1080p up to 65' long! Several sites rave about them.
I saw that Monoprice has many much cheaper, but there could be two problems:
1) pulling a cable with an end on it through the wall would be difficult if not impossible.
2) HDMI is very picky about the length of the run. People who have no problems at 15' get dropouts and other problems at 25'.
It's tough to say what will work in your situation. If you have a repeater/splitter with a good amp in it, a regular cable might get you the 50' no problem. But if you go that route, be prepared if you get sync problems at the projector (like no picture at all!)