Lucasfilm and The Walt Disney Company are working hard on making new Star Wars live-action movies, video games, books, and so forth, but it's not yet clear what the two studios have in mind for the other major Lucasfilm genre franchise, Indiana Jones. The Mouse House picked up the full rights to latter property in 2013, after buying the rights to release future movie installments from Paramount (which distributed the previous four Indiana Jones films). Presumably, the studio had a good reason for doing that.
Lucasfilm President Kathleen Kennedy, who has a long history with Steven Spielberg movie properties (one that goes back to the early 1980s), previously let it be known that a fifth Indiana Jones live-action movie will without a doubt "be made inside this company" one day in the future. However, going by the recent comment from Indiana Jones franchise producer Frank Marshall (who is married to Kennedy), the discussion necessary for that to happen has yet to really get underway.
Kennedy produced the first three Jurassic Park films, but Marshall stepped in for Jurassic World as his wife has been preoccupied with the not-so-small tasks of running Lucasfilm and re-launching the Star Wars brand. /Film thus got to interview Marshall as part of the promotional campaign for Jurassic World, where he said "there've been no discussions" about whether Harrison Ford will continue to play Indiana Jones or if Jurassic World star Chris Pratt could take over the role, as has been rumored.
Marshall, at that point, further clarified his meaning:
Yeah. I mean, we’ve had no discussions on Indy 5 to date.
AICN, meanwhile, is claiming to have heard from its spies at Lucasfilm that the company is eying a tentative December 2018 release date for the fifth Indiana Jones film. Disney Chairman Alan Horn did previously indicate that a new adventure with Dr. Jones (Jr.) won't happen until 2016 or 2017 at the earliest, so the idea of the release date being three and a half years away from now (from the time of writing this) is fairly easy to swallow. However, if that is the case, then it's further proof that Indiana Jones 5 is going to be a reboot of the franchise, simply because of Harrison Ford's age (he'll be 76 by then).
It's worth noting that both Kennedy and Horn previously claimed there's neither a script nor story for the next Indiana Jones movie yet, having emphasized that Disney and Lucasfilm are taking their time on deciding how to best move this franchise into the future. Combine that with Marshall's new comment, it suggests that no final decisions have been made about what to do with the property, nor have their necessarily been any serious planning done yet. However, it's highly doubtful that the series' producers haven't talked at all about Indiana Jones 5 yet (even in private).
Lucasfilm, in the meantime, is moving full-steam ahead with new Star Wars movies; J.J. Abrams' Star Wars: The Force Awakens is set to launch in December 2015, followed by Gareth Edwards' Anthology (read: spinoff) film Star Wars: Rogue One a year later, and Rian Johnson's Star Wars: Episode VIII in May 2017. In other words, there's not much incentive for the company to fast-track development on a new Indiana Jones movie without a clearly-defined plan in place, like the map it has designed for the upcoming Star Wars installments.
To sum up: it sounds as though Indiana Jones will live on, in one form or another, but until further notice no final decisions about how that will happen (much less who will be leading the way) have been made. Furthermore, if the 2018 release is to be believed, we might not be getting any firm answers to these questions in the immediate future. Best that everyone remains patient, for those reasons.
We'll continued to keep you updated on the status of the Indiana Jones franchise.