Death Stranding has been updated to version 1.13 today by Kojima Productions. You can find out the complete patch notes for this update from here.
According to the patch notes, this update has added the option to convert saves on the PS5. This is seen with the changelog accessible on the PS4.
Death Stranding Update 1.13 Patch Notes
- Addition of save data conversion system
Save data from the version for PlayStation 4 Death Stranding can be exported for use in the version for PlayStation 5.
Open the cuff links menu while standing at a delivery terminal, and select “Export Save Data”.
Data cannot be exported while Orders for Sam are in progress.
Complete any outstanding orders before exporting.
In order to load exported save data on PS5, you will need to login into the same account for PlayStation Network that was used to create your PS4 save data.