Both cats and dogs can travel to the UK without quarantine, but it is a 6 month process to prepare them for travel and it is relatively expensive. For 5 animals, between medical preparations and travel costs, it will set you back thousands of dollars.
Shipping a dog (a small alsatian, probably about 50 pounds) cost my friend about $2500; I don't know how much a cat would cost. I brought my cat a cheaper and more circuitous route, through France and then by ferry to the UK, but I have been informed by another friend that it this route is no longer allowed. You could call Defra and find out for sure.
If it is still allowed, Air France allows cats to travel in cabin as excess baggage for about $150 per cat, but bringing 4 cats would probably be impossible for 2 passengers, since I believe each passenger is only allowed to transport 1 animal, you'd need to check. It would be a minimum of $600 airfare for the cats alone, and that doesn't count any of the other costs that are involved with travel (trains, ferry, more trains... or car hire). Of course getting the animals microchipped, vaccinated, blood tested, and all the paperwork to prepare them for travel is expensive as well. It cost me more than $200 for one cat. Dogs I think require a further vaccine and test that the cats don't need, but I can't remember what it was.
You might also find contacting your local USDA informative, I found them very helpful, as were the folks at Defra.
You may not have much of an option, since it's unlikely that you have more than 6 months before your move at this point. You could of course allow the animals to go into quarantine. It is for 6 months (possibly you can start the process and it would only be the remainder of that 6 month period, but again I do not know for sure) and you must pay the quarantine costs. I can't imagine it would be cheap. It would also be very hard on your pets to be separated from you (and possibly each other) for so long.
You should also consider how difficult an international move is for animals. Flying from Dallas to Aberdeen will take about 13 hours perhaps more. Some animals do not travel well, and sedating them is very unsafe. If you are only going to be in the UK for 2 years, you might be better to see if a friend or relative would keep them for the duration of your stay.
Sorry I don't have happier news for you.
Best regards,
Elizabeth