While it appears that there will be a future for the Pirates of the Caribbean franchise, the only thing we really no for sure about that future is that it won't include Johnny Depp or Captain Jack Sparrow. Even the possibility of a cameo for the character in a future movie has seemingly been put to rest. This will certainly make for an interesting new movie as, for many, Captain Jack Sparrow and the Pirates of the Caribbean film franchise are pretty tightly wound together. One person who clearly feels that way is another member of the franchise, Joshamee Gibbs himself, Kevin McNally.
Kevin McNally has appeared alongside Johnny Depp in all six Pirates of the Caribbean films as Mr. Gibbs, He recently appeared on The Respondent, a YouTube series hosted by another Pirates of the Caribbean franchise member, actor Greg Ellis. The pair discussed the impending reboot of the franchise, and while McNally took no issue with the idea that the franchise might need a little refreshing, including new, younger talent, he still feels that you can, and should, make that movie and still include Jack Sparrow in some capacity. According to McNally...
My feelings about this are very complex because in a sense there was a slight feeling that the franchise itself had played out a little bit, so a reboot is a reasonable idea. I don’t think a reboot, if you concentrate on younger characters, should still exclude Jack Sparrow.
For what it's worth Kevin McNally even has an idea for how a Pirates of the Caribbean 6 could work. He suggested the film should actually focus on a search for Jack Sparrow himself. In that way, the movie could focus on a new cast of characters and make them the leads, but still allow Johnny Depp to appear, in a more limited capacity.
At this point, there are reportedly two different Pirates of the Caribbean movies in early stages of development. One is being penned by Birds of Prey writer Christina Hodson to star Margot Robbie. The other is being written by Ted Elliot and Craig Mazin. It's possible that one or both projects could still take place within the same universe as the previous five movies, Jack Sparrow might get referenced, or we might see other characters, perhaps even Joshamee Gibbs, appear in order to connect the films. Or we could see a complete reboot that uses the franchise name but tells a completely disconnected story in a world where there is no Jack Sparrow.