Nikon D5100 - "sharp" telephoto zoom lens 55-300 mm

I am not sure how you qualify "sharp", at what aperture and what technique. From a purely optical standpoint, the 55-300 is plenty sharp. You may have to step it down a bit for maximum sharpness and you need good light as it is already not a "fast" lens at 300, but with that said I don't find mine lacking in sharpness.

It is slow to focus, it has a cheap wobbly plastic barrel, it needs good light... yes these are the drawbacks but it is cheap, light, sharp and gets excellent color/contrast IMO.

These are from my 55-300