Back in the PS1 and PS2 days, Sony Computer Entertainment enjoyed the lions share of third party exclusives, with many of the biggest games those generations going exclusively to Sony. But with the PS3, that dominance was lost. A convoluted Cell Processor, plus the popularity of the Xbox 360 meant that franchises once exclusive to PlayStation, were now also popping up on Xbox. As such, the vast majority of exclusive games for the PS3, came from Sony itself.
The PS4 was an improvement however. It's easy to work with PC-based hardware, combined with its massive install base, meant that PS4 enjoyed more big exclusive or console exclusive titles from third parties than the PS3 did. Street Fighter V, Persona 5 Royal, No Man's Sky, Neir Automata, Crash N' Sane Trillogy, Final Fantasy VII Remake, Dragon Quest XI, And a variety of indie and PS VR games are all at least console exclusive to the PS4, or were timed exclusives to the system.
With reports of the PS5 being even easier to develop for than the PS4, we could see even more notable third party exclusives for it. Now let me be clear, the days of the PlayStation 2 will never be repeated again. AAA franchises just cost too much to make now for that to happen, So I don't expect things like Grand Theft Auto or Mainline Final Fantasy games to be full on exclusive. However, I can see many AA, Indie, and VR games being at least console or timed exclusive to PS5, especially if the system sells as well as or better than the PS4.