Sorry for the delay and thank you for your answer.
I'm afraid I won't give login credentials to my backend but I can provide screencaps.
I've managed to do the update in august but I don't know how I did, I suppose I found the 5.10.5 archive directly in JED or through the Joomla update but for real it's so annoying you just can't give a proper download link. Your website just link the new 6 version and just nothing about 5.10.xx.
Now I need to update to 5.10.16 version and I'm totally lost how to do it.😕