Currently there are 5 native SuperZoom lenses for Sony FX5 and all of these lenses are autofocus (AF) type.
FX5 also has a sensor based image stabilization system which means that all of these lenses will be stabilized when used on FX5.
Since Sony FX5 has environmental sealings (Weather Sealing), you may like to couple your camera with one of these 5 SuperZoom lenses with Weather Sealings.