It's pretty obvious that Pathfinder isn't going away; the only question is whether they can maintain their growth.
In the early '90s, TSR was a juggernaut; their novel lines alone were huge, and store shelves were full of myriad campaign settings. Then, White Wolf came along and ate their lunch. WoD was enormously popular and brought in massive numbers of new gamers, many of whom were (gasp!) female. ...But where is White Wolf today? People still play Vampire and such, but it's not such a big deal any more.
As TSR waned, other games became popular. GURPS was the new hotness at one point. It's still a thing but it hasn't taken over the RPG community despite being a "generic, universal, roleplaying system." Later, Savage Worlds (which I dearly love)/also flourished in the post-3.5 world (by which I mean, it seems that as players left 3e/3.5, many went to Savage Worlds). It's still going strong, but I don't see it unseating D&D any time soon. Rules-wise, I find 5e very similar to Savage Worlds in some ways, and that's probably no accident.
Ultimately I think there are some Pathfinder players who will drift to 5e, but I don't envision the reverse happening too often. It feels like 5e's "be all things to all people" approach will make it easier to sustain a player network and attract new blood. Pathfinder will always have diehard fans, but like GURPS and Champions before it, I think it will prove too crunch-heavy for lasting broad appeal.