5e D&D will last, without doubt, until sales figures flag consistently enough to warrant a new edition to rekindle interest. If you want a long-lived 5e, keep buying what's released, and keep sharing the game and the hobby with new players as long as you can.
My best guess when the flagging starts? Maybe... 2019? It's still going pretty strong, and as The UA articles have proven, there's quite a bit of design space they can mess with for a major rules expansion, so at the very least I think we're getting five to six years out of this puppy. IMHO more than a decade is unrealistic to get out of a "healthy" edition cycle; in my estimation both AD&D1 and AD&D2's cycles were a bit "unhealthy" toward the last few years of their cycles, made so extended by Gary Gygax's contentious ouster, and TSR's bad business moves, respectively.
Then again, it's been said that AD&D1 was still selling respectably into 1990, when it was forcibly killed off to keep from cannibalizing AD&D2 sales, so maybe we'll be looking at 5e books on shelves into the year 2030...