Does anyone have a solution? I dont understand, why i cant use my DS5 for playing this.

This game was released on PS4 on February 2017 and on PC on August 2020, almost 3 years and 3 months, respectively, before the realease of the DualSense. Were they able to add the support later? Yes, but it was not the case.

However, this is the PC and since HZD has native support for the DualShock 4 (wired) there is a way to play with the DualSense wirelessly and even with the PlayStation icons.

You must install DS4Windows. On Profiles make a New profile with preset options for the DualShock 4 and in the subtab Other > Virtual Controller Settings, select DualShock 4, then Save the profile. Then in the main tab Auto Profiles Add the HZD game and select the created profile in Controller 1. Now you just have to start DS4Windows and turn on the DS before the game starts and enjoy.