Which Lens will be good for my Nikon 5100?

Good steady zoom for landscape photography is my main priority.

This a hard question. It is hard to answer because every photographer is different.
for landscape and zoom get the Nikon 18-300mm lens.
It covers the whole range. It is a nice lens. It does have a big price tag.
For a little bit cheaper get the Nikon 18-200mm lens.
They are both pretty good lenses.
A Nikon 18-105 may also be a choice because of price.
I prefer to have a wide angle lens and a zoom lens just because the wide focal length lens have a bit more distortion sometimes. If you have a editing program like Adobe Lightroom you do not need to worry because it has a toll to remove distortion.

I use the 55-200mm VR lens.

For my money (paid $250.00) a refurbished 18-105mm VR Nikon lens is awesome. I used it on my D40 and when I bought a D90, it mounted perfectly and does a fantastic job!

If you want the best than the 17-55mm f2.8G is the best DX wide angle zoom. But it is quite pricey at $1300 new.

The 18-35mm is a good lens too. At $750 it is going to hit your wallet pretty hard.

A little less wide and a bit cheaper is the 24-85mm at $600

The cheapest lens I would recommend is the 35mm f1.8G. This lens is very sharp and nicely priced at $200.It is not a zoom lens but, for the money, it is a great lens.

Happy shooting