I see everyone with alot of different modes on the S5 camera but I have only 3 choices to choose from and no Zoom what so ever
You can download additional modes from the Samsung Apps app.
Unlike the S3 and S4 where you could use the volume buttons to zoom in and out, I have found with the S5 you have use two fingers on the screen to zoom in and out. Spread your fingers apart to zoom in and move them together to zoom back out.