The brightness keys don't work on the UX305 so I managed to bind Ctrl+F5/6 to execute
xdotool key --clearmodifiers XF86MonBrightness{Up/Down}
While this works fine and even shows the visual notification but the whole thing feels a little hacky. Is there a way to bind the shortcut to the actual Fn keys? Xev doesn't do anything when you press Fn+F5/6 so thats that....
I'm myself a KDE user, so I won't tell you exactly how to change the global shortcuts in Ubuntu, but I think this is what you are actually trying to do. The global shortcut for brightness change is assigned to XF86MonBrightnessUp/Down and you should be able to change it to whatever else you want, e.g. Ctrl+F5/6.
This guide seems to be describing how to do this in Ubuntu: https://help.ubuntu.com/stable/ubuntu-help/keyboard-shortcuts-set.html