The common way for Point and Shoot cameras is to zoom with a + or - button or a rocker switch while looking at the rear display or the viewfinder if it has one. That is not the case with digital SLR cameras and zoom lenses. The little P&S cameras just don't have room on the lens for this extra ring. If you are coming from a P&S camera for the first time you should read up on your camera and lens and become familiar with how all the controls work. And as Brian mentioned not all lenses for SLR cameras are zoom lenses.
Enjoy your D5100 camera. It will take beautiful photos for you. But become familiar with how it works at the same time. And use the viewfinder for your zooming and composition. It's the better way to go when hand holding the camera
Ah, but if your camera is on a tripod and your target is stationary and you are using manual focus, using the zoom on the display will allow you to get extra crispy focus. I shoot birds with a telephoto lens. First I set up a target in the expected flight path and focus on it using manual focus and the display zoomed all the way in. I then remove the target and wait for the action to begin.
Of course, depth of field on a 500mm lens on a 5100 at 10 ft is less than 3 inches so there are a lot of throw away pix. But when the flight path is just right, you can get some nice pix.
I also use the same technique with portraits. In that case, the subject's eye is the target. Same for still life's and macros.
Be sure to zoom back out to check your composition. It's a bit of a shock when expecting to get just the polllen of a flower and getting the whole flower. (Although my "Flying Hybiscus" was a rather pleasant shock)