Great news! You can use your DualShock PS4 controller on your brand new shiny PS5, but not if you want to play a brand new shiny PS5 game. This makes sense. Players will get a PS5 DualSense controller with the console but could possibly save their coin on another one by using their old DualShock controller. The DualShock controller will work on PS4 games played on the PS5, according to a PlayStation blog.
But what was interesting in the blog was that licensed products like racing wheels, flight sticks, and arcade sticks will work with PS5 games. This was something to be speculated on due to a lot of peripherals working on the PS3 as well as the PS4, raising the question if they would carry over to another generation.
Tech can become obsolete after four or five years. Making a component last a decade needs a lot of parties to work together. With backward compatibility being a huge part of the next console generation, it seems important that peripherals carry over with the games.
The DualSense controller should be primary on the PS5 with its new features anyways.