Many PS4 Dirt 5 players were wondering if they will be able to transfer their saves to the new hardware and we now have an answer. Unfortunately, the answer is "no". Once you upgrade to the PS5 version of the game (you can do it for free, btw), that's it and you'll have to start from scratch.
Here's the explanation of Codemasters: "Currently on Xbox, all progress can be carried over between generations. On PlayStation, your Playgrounds creations can be carried over, but other game progress (Career, currency, saved liveries) cannot. If that changes, we'll let you know!"
It sucks really but what can you do. At least you have the freedom of choice.