If overall current is low - where should the energy to destroy the display come from?
Sorry - but you where wrong in the first place with the MOSFET - and now again there must be some mistake in your thoughts because I do not get 320mA. I don't know what's wrong with your calculation (only that I don't have a glue where the display should get 5V - I don't attach it to 5V since there is no pin for 5V) and I don't care (to be honest). I appreciate your help even it did not lead in any helpful direction. I can also not explain why my display works now but it didn't in the first place but honestly: what part do you have in that? Obviously your assumption that I need a resistor + MOSFET was wrong.
I am done with this topic. Yes - I have to live with my display's lifetime and I will.