I think those hoping for Obsidian or Inxile to make Fallout 5 are out of touch with reality and with the demands of modern video game development, in reality if Microsoft really wants another studio to make a Fallout 5 their only option would be one of the COD studios. Although allowing them to make Fallout 5 brings out the question of how Microsoft can keep the COD game a year pipeline.
Rather than handing off development of Fallout 5 to another studio, which would disappoint Bethesda Softworks while requiring that someone else further develop Bethesda's Gamebryo engine, Microsoft should look to Fallout: New Vegas for inspiration. InXile should have already been told to complete Clockwork Revolution before the end of this year, while given whatever resources are necessary to accomplish that, and then been instructed to create a Fallout: New New Orleans with the Fallout 4 game engine (or perhaps the later Starfield version of Bethesda's Gamebryo engine, or both), in a limited amount of time (no more than two years), so that it will be released well before The Elder Scrolls VI, much less Fallout 5.