My take on the Big 6 studios through their next 5 years of release (end of 2022):
Disney: Disney is in the best shape by far. Not only do they have a very clear release plan through 2020, they have so many redundancies that even if one or two of their initiatives starts to dry up by 2021/2022 the other studios can pick up the slack. While more than one studio would kill for more than a single dependable studio/line of films, Disney currently has 5 (Marvel, Star Wars, their live action fairy tale stuff, Pixar, and Disney Animation). I'm not sure if their other big budget live action attempts will pay off, but with so much guaranteed income, they can afford to take a few risks.
Marvel and Star Wars are both golden through the rest of this decade. I have no idea what is planned for the MCU after Avengers 4 (other than a third GotG and another Spider-Man for Sony), but they haven't even gotten into sequels for Doctor Strange, and Black Panther looks like another promising start. We'll see how Captain Marvel does in a couple of years. Star Wars is in a similar position. Disney might want to hold off on Eps X-XII for a few years, but there are nearly limitless directions that the side films can go. I don't think that the Star Wars films can indefinitely stay over that $500M+ mark domestically, but they can pretty much halve that and still be doing well. Especially if we start getting cheaper entries.
I am hoping that Disney Animation will transition into sequelizing their output in the next 5 years to give Pixar some time to build up more original releases. I could see us getting another Dory film near the end of the next 5 years. Toy Story seems to be on a 10 year cycle. Cars should probably be retired or moved to the small screen.
Warner Bros: While Universal might have more goingfor it in the short term, I think that WB is the second best off going beyond the next 5 years. The DCEU is clearly very popular, and is young enough that WB easily has 5 years left in it before they have to worry about too many shake ups.
I'm not sure if Fantastic Beasts will power through 5 films (or whatever number they were throwing out last fall), but the Harry Potter brand is one of the strongest out there. Easily top 5 among the live action stuff. If people get sick of the prequel stuff, they can always transition to actual sequel material, be that adapting the Cursed Child, or going a different route.
Beyond those two franchises, WB has their part in the Godzilla/Kong monster films, their LEGO films (we'll see how Lego 2 does next year), and a wide assortment of director-oriented films in their schedule (Nolan is almost his own brand if they can keep him happy). There's also the potential to try and relaunch the Matrix if they feel the need for another ongoing franchise.
Universal: I think that Universal's live-action line up will start to age out by the end of the next 5 year period, but they are definitely well on their way to establishing themselves as a major rival to Disney in the Animation space. Even if the shine is coming off the Minions franchise, Illumination is on an amazing box office streak at the moment, giving them plenty of sequels to exploit. Add the library and talent that Dreamworks Animation offers to that (along with Universal's much better marketing strategy), and there's plenty to last out the next half decade.
I think that Fast 9 has a pretty good shot at >$1B worldwide still, but I'm sensing a crash for the franchise shortly after that. We might get Fast 10 and that Rock/Statham spin-off to still decent results, but you can only do the same thing with the same people so many times before audiences move on (as we have been seeing in the past 2 years). Still, that takes them through at least 2021. Jurassic World will get a third film in 2021 or so, but I think that franchise risks repeating what happened to the original set of sequels unless they find a way to really mix up the formula.
Fifty Shades and Pitch Perfect are done within the next year, but they aren't so big that they can't be replaced. The Dark Universe stuff seems DOA, but I expect Universal to make another couple of attempts to get it off the ground. Perhaps with smaller budgets. I have no idea how their partnership stuff with Legendary will go, especially now that Legendary has new owners in China. Pacific Rim 2 seems like a waste of money, but who knows. Universal always does well with the low and mid budget stuff. No reason to think that won't hold true in 5 years.
20th Century Fox: The X-Franchise is as strong as it ever was, and even Fox will have a tough time completely killing it before the early 2020s. Deadpool will get a second sequel in 2020 or 2021. There's plenty more that they could do with the X-Men universe, especially if they sweep aside the approaching 20 year old Singer continuity. They don't even have to reboot per-se. Just stop acknowledging some of the earlier stuff as the existing actors end their contracts. As for Fantastic Four, I would like to believe that the rumors are not true, but who knows. They could try a second reboot to keep the license.
AVATAR is clearly Fox's big hope for the 2020s. I think that we have talked about it enough. Until we are close enough to release that we are actually getting footage, it's hard to make any predictions beyond "the first sequel will probably make a lot of money".
I am not sure how the other aspects of Fox's announced live action lineup will go. They have a ton of projects in the pipeline running the full range of budgets. It also seems like they are taking a few more stabs as the Young Adult(ish) Sci Fi genre. Maybe 1-2 of those will pan out. Maybe not. Blue Sky lost Ice Age, but they are still pretty reliable for mid-budget animation.
Sony: There's a big gap between Sony and the previous four studios. They are betting the farm on Spider-Man, because that's pretty much their only mega-franchise. I'm not really sure how that will work out for them beyond the two Marvel produced films though. Sony has been in a transition period, so I guess they get some benefit of the doubt, but saying that Spider-man has been mismanaged in the past is an understatement. I guess getting a film out there for less than $220M is a good first step.
I don't have much confidence for any of Sony's announced larger budget stuff outside of Spider-Man. We have The Dark Tower and Jumanji this year, and a Charlie's Angels and He-man reboot on the horizon. Sony had great luck with the first two Jump Street movies, but there has been major feet dragging in regards to a third film. We're already looking at a gap of what? 4.5-5 years at best? At some point, it will be too late for people to care. Sony also has Men in Black. However, that is super expensive with Will Smith, and of unknown strength without him. Sony typically does well with their low budget stuff, especially the films targeting ignored demographics. That should continue to work for them.
Sony Pictures Animation also seems to do alright in the mid-budget range. Hotel Transylvania has one more film left, and they have several other projects announced that could do alright for the price tag. I just don't see much from the live action or animation line up that screams $600M+. I suppose it is possible that they could strike lightning with something unannounced in 2020-2022, but they need to start showing serious results before that point first.
Paramount: Paramount has been desperately pursuing Chinese co-financing for their blockbusters for a year or two now. The problem of course is that there is little of proven worth beyond their aging franchises.
Transformers is on a serious decline, to the point that its future is uncertain beyond maybe one more film if they don't manage a course correction. Yes, Transformers has the generational appeal that will allow for a reboot down the road, but that requires a cooldown period.
I think that the Mission Impossible series has hit its apex and now is on the way down. Ghost Protocol gave it a shot in the arm, but I don't think it is reasonable to expect a repeat of that. Tthe next one will still do pretty well, but how many more of these can Cruise sell? Like Matt Damon and the Bourne stuff, I don't think Mission Impossible has any real life post-Cruise either.
TMNT failed. Terminator failed. GitS failed. Jack Reacher went nowhere. Feature film Star Trek went from being the biggest (domestic) relaunch ever to life support in 7 years. I'm not sure what else they have left. I guess they can try some sort of Hasbro shared universe. Paramount does pretty well with low/mid-budget prestige stuff, but I don't see how that differentiates them from Lionsgate, or the many boutique studios/distributors.