It seems incredibly unlikely that id Tech 5 would be open-source to the community in the form that id Tech 3 and the older engines are provided free of charge to the community. id Software hasn't even opened up id Tech 4 yet, but that's expected to take place this calendar year. However, it was pointed out in our forums this morning that the Rage site clearly says id Tech 5 is open-source.
A graphic on this web-page for id Software's Rage game clearly states the engine is open-source. The graphic is also copied below, but it says "id Tech 5; Developed by id Software, id Tech 5 is an advanced open source engine capable of creating incredible environments."
While we're sure id Tech 5 will eventually be open-source years down the road, this would be extremely surprising if id Tech 5 is open-source (in the traditional context) immediately. We've reached out to id Software to find out if this is a big mistake on the part of their marketing / web department or whether there is actually an open-source surprise.
Regardless, this year we will likely see id Tech 4 at least go open-source (most likely at their annual QuakeCon this summer; at least year's QuakeCon is when they open-sourced ET and RTCW) and the Rage game is slated for release this September. The id Tech 5 engine and Rage game will work with Linux, but possibly not right out of the starting gate.
Besides Rage, id's Doom 4 will also be based upon id Tech 5. It's also expected to be licensed to third-parties as a proprietary engine, which makes this open-source news even more surprising.