The tools for 4th edition will stay online as long a people continue to pay for them. D&D insider will continue to be a subscription service for 4th edition content (compendium, character builder, Dungeon and Dragon mags) only.
The digital tools for 5th edition are being developed seperately by a company called Trap Door Technologies (TDT). The website for those tools can be found here.
The tool is called Dungeon Scape and will be available soon as a beta that includes only the player portion (character building), with DM content, and a homebrew tool set releasing later.
The TDT team have been updating their blog regularly and have announced that the pay model will be a free app (on web, iOS and andriod), with content coming via a la cart or bundled purchases (prices not announced). Much more of the known details can be found here.
Lastly, as we've already seen, they are trying really hard to make it so BD&D is all you need to play their published adventures (or your own game). We have the BD&D players book, and the BD&D DM's book. As well as supplements for each of their adventures that includes the monsters from the Monster Manual that aren't in BD&D. This provides a searchable rules set as a subset of the full game. (The Basic rules are basically all of the PHB rules content with a subset of the classes and spells).