Eventually, any game will get stale and warty. Interest will decline as people move on to new things. I'd say ten or so years is the average lifespan of a well-regarded game.
But, it may not require a new edition to reinvigorate 5E when that time comes. Just a change of setting, which alters the flavor of the game.
That said, I'm sure we'll get a revised PHB someday. Mearls has already mentioned on a couple occasions what that process would look like. They take the survey data that they keep gathering, and find weak parts of the game, like the Ranger. They iterate on an alternate version, and release it in a new product. Someday, if the new version becomes dominant in actual play, they might revise the PHB to include it instead.
It seems obvious from the Unearthed Arcana articles that they're probably working on new books with alternative class builds and so on. I just don't expect it to be called the PHB 2 or anything like that since they want to avoid confusion with people thinking they can buy just the version 2 of the book and thinking they would have all the rules.
But a book with a bunch of class variants? Maybe a new DM's options book? I expect to see that in the next year or so.