Fortnite always shows its existence free of cost on every platform. Epic Games has never asked for money to download Fortnite. Though Fortnite has in-built purchasable kinds of stuff.
Is Fortnite Available In PS5?
If you are a PS4 user with Fortnite, then there is no mentioning of Fortnite in the list of those games which aren't playable from PS4 to PS5. So the offline version of Fortnite is going to be backwards compatible with PS5. I talked about Fortnite Save The World. You must know that only the games of PS4 are going to be supported in PS5 in the name of backward compatibility, not the PS3, 2, and 1. Although there's no Fortnite in PS3, 2, and 1.
After all, PS5 is just a successor of PS4 Pro having some upgradation. It won't be like that it is just made to play its own separate new games available in the market exclusively for PS5.
Conclusion:
Fortnite offline version is available for PS5, though not free if you don't have it on PS4.
What about Fortnite Battle Royale?
Fortnite Battle Royale is absolutely free to play on PS5. Just like PS4, Xbox One, PC, Mobile, and Nintendo having free-to-play Fortnite game, PS5 have free-to-play Fortnite. On the other hand, Fortnite Battle Royale is one of the most popular battle Royale games, so there is no possible chance for Sony to cut out Fortnite from PS5 as well as from Xbox Series X.
Conclusion:
Fortnite Battle Royale is free to play on PS5, you can download it from PS Store.
When did Fortnite release on PS5?
Fortnite was released on PS5 on 12th November 2020 in major countries. Just on the release of PS5 in some countries. While in the rest of the countries, Fortnite was released on 19th November 2020.
About smoothness and quality of Fortnite in PS5:
PS5 has hardware that enables games to run at 4k, with up to 60 FPS. If lower down the resolution, it can even touch 120 FPS. Fortnite is a competitive game, so graphics don't really matter as compared to offline games.
So in terms of smoothness, PS5 can definitely run Fortnite at 60+ FPS. By the word 60+, it can even touch 100. Looking at the specs, RDNA 2 (custom) can touch up to 60 FPS on 4k resolution on paper.
Moreover, 4k HDR with 120 FPS is certainly not possible with current-gen hardware. If it was possible, then it will require around 50 gb/s of speed, which is too much, and certainly, not everyone got an ultra-high internet connection. Currently, even 1gb/s is out of reach for most people around the world.
So 4k resolution with 120 FPS is just any other dream-like PS5 backward compatibility with PS3. So Fortnite can be either run at 4k resolution or with up to 120 FPS (on paper, in reality, even 120 FPS won't be possible) and both cannot happen simultaneously.
Though my purpose is not to ruin your mood by bringing out these demerits, wanted to make you realize that grass is greener on one side, and those fairy tales which Sony said during the initial time were fake. After all, Fortnite is a competitive game that is free to play on PS5
About Cross-platform in Fortnite for PS5:
Yes, Fortnite is going to support a cross-platform feature for PS5. Fortnite is available on all platforms, from mobile to Nintendo, and till now all the platforms support cross-play features in Fortnite. Even the Xbox X series players can cross-play Fortnite with PS5 players. One can play in a team of Fortnite having mobile players as well as PS5. So think Fortnite of a fully cross-platform game.
Epic Games makes a lot of money by having Fortnite to be able to run on every platform with crossplay included enabling one to play Fortnite on a PS4-Xbox One-Switch-PC and even mobile devices. Surely Epic Games would want to continue the Fortnite craze going by releasing it on major next-generation platforms.
Conclusion
Fortnite is available for free of cost in PS5. One can download Fortnite on PS5 without paying a single cent. It's a free-to-play battle royale game available in PS Store. It supports cross-platform, which means you can play Fortnite on PS5 with players playing from another platform such as Xbox X Series, Xbox One, PS4, Mobile, and Nintendo. Epic Games is surely using a really good technique to get more attention and the term free to play and 'cross-platform' has done the job for Epic Games which in turn yields out million more people.