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 were being developed seperately by a company called Trap Door Technologies (TDT). The website for those tools can be found here (note, this now redirects to a page that discusses how they no longer have a relationship with WOTC).
The tool was called Dungeon Scape and was briefly available as a beta that included only character construction, with DM content, and a homebrew tool set releasing later.
The TDT team had been updating their blog regularly and had announced that the pay model will be a free app (on web, iOS and Android), with content coming via a la cart or bundled purchases (prices not announced).
WOTC has not announced their next move on what the future of digital tools will be for 5e, but have indicated that they do intend to develop something...eventually.
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).