Looking at new lenses for after Christmas, I have come across three that I like. They all come in around $500 or so used. I do mainly G&N with d5200.
Tamron 70-200 VC
Sigma 70-200 non OS
The Sigma 50-150 being DX and the other two being FX. I have no problem with the DX as I dont plan on upgrading to FX anytime soon. This would become my main lens as well, Id keep my 18-55 and still hang on to the 55-200 for a backup for the time being.
I know one of the big things with the Sigmas is the reverse focus/zoom from normal Nikons, but I dont think it would bother me to much.