OK, if I have F-key set as system key, only Fn+F5 or FN+F6 can be used. Fn+ F13 up to 15 don't work. But in such configuration F5 or F6 alone still won't work (I must press with FN).
So maybe You could add possibility for such actions? For exemple, I use CopyLess 2, and if I choose F13 alone it works perfect and my system F-keys are still OK.