I just bought the Galaxy S5 Neo and this menu thing was really annoying me mainly as I use an important app which is outdated and has no 'menu' button on the screen. I spent like 2 hours trying to discover a solution and finally come up with the following:
Go to: Settings / Personal / Accessibility / Dexterity and interaction and press 'Assistant Menu'. Enable this function and a separate button will appear on the screen (all the time) but with it you can access those 'hidden' menu functions.
Hope it helps!