What lens should i buy for Nikon D5200 For Fashion Photography ?

Good answer from Joe.

The lenses he lists (24-70mm, 70-200mm, 50mm, 85mm) are what I use.

What makes you think there is just one. 24-70mm, 70-200mm, 50mm, 85mm, etc.

Others have suggested
Canon EF 85mm f/1.2 L II USM lens
Canon EF 135mm f/2.0 L USM lens
Canon EF 24-105mm f/4 L IS USM lens

It depends on your style,

24-70mm f/2.8 is my goto for fashion... 70-200mm for either close up or more distant subjects.

70mm to 200mm is telephoto only - starts longer than your 55mm that you already have. Thus likely to be too long in a studio for full length. Nice to use in the "great outdoors" if you have the space.

Really it depends on your style of photography. Do a couple of practice fashion shoots using the 18mm to 55mm which you have (I assume) at present, and see where in its range you like to use it. For "natural" good portrait-style photos you will most likely not be using it shorter than about 30mm, longer for head and shoulder or detail shots.

A 50mm might suit you nicely, as long as you have enough studio length to use it for full length shots.

IF you can only afford one lens right now (they're not that affordable), I'd suggst the 28-70mm f/2.8 as Frank suggested, and save to get the next lens that would be the 70-200mm f/2.8, as Frank also suggested. The very next lens, following the mentioned zoom lenses would be the 50mm f/1.4 or 50mm f/1.8 (primes). Deep Blue has a very nice collection (or "arsenal") of lenses, REALLY nice!

I would use a standard zoom like a 24-75 f/2.8 or 28-70 f/2.8, along with a 70-200 f/2.8. Zooms allow for greater versatility and faster workflow. Having an 85mm f/1.4 or 50mm f/1.4 is also useful depending upon your needs and style. I would much rather start off with fast f/2.8 zooms than primes, and then add a prime or two as I go along.

18-135mm