Question about Nikon AF-S Nikkor 14-24mm f/2.8G ED

The lens is for FX cameras. You lose wide-angle on the D5500. There is a DX wide-angle lens for the Nikon D5500: the Nikon 12-24mm f1:4G. It is cheaper than the FX lens.

Yes, that should work. I have a Nikon D90 and it works perfectly. The photos turn out very well.
I can only recommend the lens.

Functionally, there's nothing to be said against it, but from my point of view it's more a question of philosophy.
The Nikkor 14-24mm f/2.8 wide-angle zoom is one of the best on the market, even when fully opened it is crisp and sharp right into the corners of the image. That has to be the case, a fast lens stands and falls with this characteristic.
On an APS-C camera, however, this FX property cannot be fully utilised because of the image cropping on the sensor side. At the same time, it is a heavy and expensive piece of glass on a rather lightweight camera. I would consider whether the DX 12-24mm f/4.0 might be an alternative, especially for travelling. These extreme focal lengths are rarely needed. For weight-conscious travellers there is always the possibility of taking two three shots with the omnipresent 24-70mm and then making a panorama at home.

Supposedly one of the best WW's. It is not without reason that it is often screwed onto Canon via an adapter ;)