I should add that a cat should be easily distinguished from a fox. This is true even if it is dark and the shooter is 'lamping'. The eyes have a different coloured hue (red for foxes and green for dogs/cats).
I remember a potentially devastating moment when my father was lamping and saw a pair of eyes in the hedge. He looked down the sites and closed in to accurately identify who the eyes belonged to. There was a drunk tramp sleeping in a sleeping bag. This highlights why marksmen should ALWAYS identify what they are shooting at before shooting.
Also, I should add that a 'pack' of foxes simply isn't possible. At this time of year the cubs can be quite large and will be seen with Mum and Dad. This is most likely why you saw 5 in one place. If the family have raised 3 strong healthy cubs, they will almost certainly look at easy pickings like chickens. Foxes are strictly terratorial so, really, they should only be culled where they are causing considerable problems, particularly in winter. I have found that by ensuring you have a suitably nervous/shy vixen in your area, if you leave her alone, she will keep away any potentially bolder (chicken-stealing) vixens (in winter).