Your Dirt 5 progress won't carry over from PS4 to PS5
This is sadly looking more and more like a trend.
Microsoft and Sony have chosen very different strategies when it comes to the introduction of the next generation. Where Microsoft has Smart Delivery with free upgrades and use of your save file regardless of which Xbox you play in, it is more case by case for Sony.
In a couple of games recently (like Spider-Man and Yakuza: Like a Dragon), it has been confirmed that you won't be able to use your PlayStation 4 save file for PlayStation 5 upgrade, and now yet another game has been added to that list, as Codemasters has confirmed on Twitter that Dirt 5 does not support this:
"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!"