Without seeing any sample pictures, it sounds to me like you are having issues with camera movement. The longer the focal length of the lens when you take a picture, the greater effect the same amount of camera movement will have on blur.

There are a few things you can do to reduce the amount of camera movement and the effect it has on your pictures:

• Use a faster shutter speed (Tv). This probably means taking the camera out of Auto and learning how to use one of the P A S M modes. The old general rule of thumb was to use a Tv no slower than 1/focal length when shooting handheld. With the emergence of DSLRs with sensors smaller than a frame of 35mm film the sensor size must also be taken into account. With your D5100 the sensor has a crop factor of 1.5x, so the formula for the minimum Tv should be 1/(1.5 X focal length). If your lens is at 200mm, that means a Shutter speed of 1/300 second or faster. At 300mm, you need a Tv of 1/450 sec or faster. With a 55mm focal length, 1/80 sec. or faster should work.
• Increase the ISO sensitivity your camera is using. Most cameras will produce the best image quality (IQ) at ISO 100. Increasing the ISO sensitivity will allow you to use faster shutter speeds at the same aperture, but this will also increase the amount of noise. Your D5100 has pretty good noise reduction (NR), but the higher the ISO setting, the more NR needs to be applied and this affects the overall sharpness of the image.
• Increase the size of the aperture. The lower the f-number, the wider the aperture. A setting of f/2.8 lets in twice as much light as f/4, which in turn lets in twice as much light as f/5.6. The more light you allow in, the faster the Tv you can use with the same ISO setting. That is why lenses with maximum apertures of around f/2.8 or wider are referred to as fast glass. In the case of kit lenses that come with many cameras, the problem is that at the widest focal lengths they can only open up to f/3.5 or f/4 and at the longer end they are usually at f/5.6.
• Practice good camera stabilization techniques. Hold the viewfinder up to your eye and keep both elbows in as close to your body as you can. Support the camera with your left hand under the barrel of the lens. Forget the "dirty diaper" grip you probably used with a compact camera. Live View on a DSLR is meant for use with a tripod. Stand with your feet apart and one slightly ahead of the other. Take a deep breath and exhale slowly, taking the shot just before all the air is gone from your lungs. Lean against a sturdy wall, tree trunk, building support pole, etc. to help stabilize your camera.
• Use Vibration Reduction (VR) if your lens has it. This will allow you to handhold 1 to 3 stops slower than the 1/focal length rule. You will still need to practice good camera stabilization techniques to get the benefit of VR. If you are using a focal length of 200mm, you can now use a Tv as low as 1/80, 1/50, or even 1/40 seconds.
• Use a stable platform to support your camera. Normally this means a tripod, but you can also use a bean bag on a table or even set the camera directly on a stable surface if it will point in the direction you wish. Activating the shutter via the self-timer or a wired or wireless remote will enable you to use the tripod to its full potential. When a tripod isn't practical or allowed, a monopod can be very helpful and buy you a few more stops.