This lens is compatible with the D5500. However, the lens is built for full-frame cameras. It is therefore larger and heavier than it needs to be for this camera. If you ever plan to switch to a full frame camera like the Nikon D750 Nikon D750 Body (24.30MP, 6.50FPS, WLAN) I would consider it.

As an alternative, this lens would be suitable: Sigma 17-70mm F/2.8-4.0 DC OS HSM Macro C, Nikon F DX