Best telephoto lens for the Nikon D5100?
Http://www.amazon.com/Tamron-70-300mm-4-0-5-6-Macro-Digital/dp/B0012UUP02
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If you are going to compare the Tamron 70-300 mm to a Nikkor lens, you need to compare it to the AF-S 70-300 mm Nikkor VR lens.
The actual question, what is the best telephoto lens for the Nikon D5100 is this:
The best lens depends upon the subjects you are shooting.
Which lens brand will last the longest? Nikkor can last for decades. Third party lenses start to slow focus and their apertures can start to get sluggish when shooting using small apertures.
I'd go for the Nikon because it has VR and it's Nikon.
Take a Nikon Lens, it has more benefits and will become handy for you at different levels. It is the best to go for while upgrading yourself to the Telephoto Lens.
Tamron may be cheaper but it can't replace the VR effect of Nikon. So thumbs up for Nikon VR Lens.