The Galaxy S5 is by no means a small phone and neither does it try to feel like one with its 5.1-inches display and the huge bezels surrounding it. The Galaxy S4 was pushing the boundaries for one-handed usage and the S5 crosses it. I guess Samsung realised this and included a one-handed software mode on it, as seen on the Galaxy Note 3. 

Under this mode, the contents of the screen are reduced in size and then aligned to the right or left edges of the display as if they are in a ‘window’ mode. A small on-screen navigation bar will also pop up at the bottom along with buttons to increase or decrease the ringer volume for easy one-handed operation. You can also enable access to a customisable list shortcuts to some of the frequently used apps or contacts like Dialler, Internet or Calculator by tapping the drawer or people button located at the top.

You can toggle the shortcuts on the right of the screen or replace them with access to frequently used contacts.

You can enable one-handed mode on the Galaxy S5 by heading over to Settings -> One-handed operation (located under Sound and Display) and toggling the switch to on position. After this, quickly swipe your thumb from the right or left edge of the screen to the centre and back to enable it. You can use this gesture almost anywhere in the OS to activate the mode now.

Keep in mind that the contents of the screen will align to the same edge from where you start the swiping procedure. If you think that the contents under the one-handed mode are a bit too small, you can increase its dimensions by dragging the top right or left part of the window.