The next God of War game is still a ways off but the wait won't be nearly as long as expected. Before the soft reboot of the series, with PS4's God of War, the last released game in the franchise was God of War: Ascension. Ascension, a prequel that received generally positive reviews, released in 2013. This makes it five years since the series has seen a mainline entry, not counting the PS4 remake of God of War 3 that released in 2015.
The next entry in the franchise is still something full of mystery, even given the ominous ending tease of God of War. Yet, series director, Cory Barlog, is confident that the next God of War, no matter what it's eventually called, won't release in another half a decade.
In an interview with Kotaku, Barlog discussed the tentative plans for the future of God of War. After Barlog explained that he has ideas for potentially five games in the series, not necessarily that five games will be released, the outlet joked that it would take 25 years to see the new era of God of War conclude. Barlog clarified that things wouldn't last nearly that long. There was a very specific reason for the long wait between Ascension and 2018's God of War. Barlog explained:
"A big portion of the five years was, we had to start from scratch. We had a core engine but we really redid a lot of stuff. The previous God of War games, when we went from God of War 1 to God of War 2, the core engine was there ... On this one, everything really needed to be redone, because we just had torn the engine apart in so many different ways..."
This makes perfect sense. The recently released God of War isn't just a departure for the series in terms of tone and story. God of War doesn't just bring Kratos into Norse mythology, moving him from Greek myth; the combat mechanics and set-up of the game are also wildly different than that of the previous chapters. Now that the core base has been set up, the next entry in God of War series will probably be akin to the wait between God of War 1 and God of War 2.
God of War 1 was released in 2005 for the PlayStation 2, and God of War 2 released just two years later in 2007. In 2010, God of War 3 released on the PS3, followed by Ascension in 2013. Notably, there is a jump in console generations for the series. God of War 3 and Ascension both released on the PlayStation 3, not the PlayStation 2. Yet, all three mainline games (and the prequel spin-off) used roughly the same engine.
With this in mind, it can be estimated that God of War 5 will probably release sometime in 2020 or, at the latest, 2021... hopefully. This would put it in line with the previous release schedule of the series as well as Barlog's tentative estimation that it won't take another five years to continue the story of Kratos and his son Arteus. It's a guess, but an educated one.
The real question, though, is if God of War 5 will release on PlayStation 4 or PlayStation 5. The existence of the PlayStation 5 is even more mysterious than the next entry in the God of War franchise, but there are rumors the PlayStation 5 could release in 2020. It's possible that God of War 5 could become a launch title for the PlayStation 5 since it would undoubtedly cause a great buzz and interest in a new system.
However, God of War 2 released very late into the PlayStation 2's life. God of War 2's primary release was on the PlayStation 2 despite releasing a year after the PlayStation 3 first hit the market. Seeing as the PlayStation 2 was nearly as successful as the PlayStation 4, in terms of sales, it wouldn't be unreasonable for God of War 5 to release on PlayStation 4, even if the PlayStation 5 is released or imminently releasing. After all, Sony doesn't mind releasing some of their best titles towards the end of console generations only to re-release those games on the next generation (see: The Last of Us).
Again, this is pure speculation. It'll probably be awhile until there are any firm announcements about the next God of War, let alone the PlayStation 5. Although, given the extraordinary success of the most recent entry, a new God of War is most certainly coming. Fans just have to be a little patient - though not as patient as they were waiting for 2018's entry in the series.