On most maps, you must hide in the brush before you can teleport back to your base. You can do this in 5v5 as well, but there are other ways to teleport that don't require you to hide in the brush first.
Teleport to Teammates/Turrets
To teleport to teammates or turrets, place your finger on the minimap, then drag the screen to the teammate or turret that you'd like to teleport to. Then tap the "TP" button that appears on the left side of the screen.
You can also move the camera view by tapping the "ScreenLock" button in the upper left corner, then dragging the game screen directly to your destination teammate or turret. This is slower, but more accurate, as you can take your finger off the screen and the view will stay where you put it instead of moving back to your champion.
If you buy a pair of Empowered Boots from the item store, you can reduce the cooldown on your teleports. There are Empowered versions of all the normal boots, and they are located in the Movement section of the store.
Teleport to Base
To teleport back to your base, swipe your finger downwards along the right side of the screen, next to your ability icons.