In a recent earnings report, Take-Two Interactive addressed a few questions regarding the upcoming next-gen port of Grand Theft Auto 5, which will bring the game to yet another two platforms, with PS5 and Xbox Series X versions launching in 2021.
When the new ports were announced, Rockstar already clarified that the new ports will feature exclusive content in GTA Online, and that this content will also be available on PC. This approach mirrors the Xbox One and PlayStation 4 port's content support cycle, which eventually left the Xbox 360 and PS3 behind.

During the earnings call, which also revealed that GTA 5 has shipped a wild 135 million units worldwide, Karl Slatoff, president of Take-Two, reiterated and confirmed this piece of information.
What we don't know, however, is whether the switch will happen immediately upon release, or if there will be a brief overlap period during which DLC is released on both current and next-gen consoles.
There was some overlap during the previous generation change, with a few bigger GTA Online DLCs launching on Xbox 360 and PS3 concurrently with Xbox One and PS4. Eventually, however, the hardware limitations of the old consoles forced Rockstar to make content support exclusive to the newer platforms, as well as PC of course which doesn't have generation-based hardware specifications.