Dominik, thank you!
Now I understood the content of what you were saying.
Also described here in depth:
https://www.raspberrypi.com/documentation/computers/raspberry-pi.html#typical-power-requirements
The Pi5 is delivering only 0,6A, as long as none original Power Supply 27W is connected. Obviously I have used a stronger supply with 60W for my setup with Penta Sata hat, 4 SATA SSD’s, fan unit top, fan for the Pi5 and USB-Ethernet 2,5Gbit Adapter.
By telling the Pi5 to use 1,6A instead of 0,6A, the 2,5" USB drive is now working.
In short:
sudo nano /boot/firmware/config.txt
add the line at the end:
usb_max_current_enable=1
save and reboot and it should work as Dominik suggested.
Check after reboot if it is enabled:
vcgencmd get_config usb_max_current_enable
Great, thanks again Dominik, you had the right feeling of the existing problem!