I've installed Ubuntu 16.04 on my Asus X555LJ.
But I don't know how to install drivers or how to enable function keys to controls screen backlight brightness.
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It seems quite common for brightness Fn keys to not work on Asus machines. On my Asus X205TA the brightness function keys don't work natively but I can use xbacklight as a workaround:
sudo apt install xbacklight
get current brightness:
set brightness to 50%
xbacklight -set 50
increase brightness by 10%
xbacklight -inc 10
decrease by 10%
xbacklight -dec 10
If these work, you can get the function keys to change brightness by assigning them as shortcuts to the commands.
In keyboard settings click Custom Shortcuts and click the + button to add a new one
Command: xbacklight -inc 15
Click OK, then click where it says 'Disabled' next to the new shortcut and press the key combination you want (Fn will probably not work) for example ctrl+F6 or just F6
Command: xbacklight -dec 15
And make this one F5 or whatever combination you want.