During the entire Switch generation, Nintendo's Joy-Cons have been suffering from drifting, which is basically when there's input on the analogue sticks even when you don't touch them. This makes characters walk, menus scroll and cars turn all the time. It has gone so far that Nintendo has a class action lawsuit because of this. Microsoft has also had some problems as well, mainly with the Elite controllers, and now it seems like it is Sony's turn.
Kotaku has published a report that says people started reporting that the controllers for PlayStation 5 were drifting just ten days after the console was released, and shows several examples of this (like this one or this one) proving that it is not isolated cases. Unfortunately, Kotaku adds that the chances of getting help is quite slim at the moment as Sony is swamped with PlayStation 5 requests at the moment.
According to Sony in the US, this is covered by the warranty, but you have to pay for the shipping of the controller to Sony with no refund. This could work differently in other countries as the laws for consumers differ.
Have you experienced any issues with your PlayStation 5 controller?