Since I found no answer for my question, neither in older posts nor in other forums, I want to ask the stackoverflow community for advice.
I am using a raspberry pi 3B
In my case it helped to update pip from verion 18 to the newest, in my case 20.2 (python -m pip install --upgrade pip) and then do a pip install PyQt5.
python -m pip install --upgrade pip
pip install PyQt5