Simple. Pay £5000 minus (your current credit limit) into your barclaycard account and then your barclaycard will be in credit. Then use it to pay them. Warning, don't pay the whole £5000 into your barclaycard, pay as little as possible to ensure the payment goes through. You need part of the funding to be on (barclaycard) credit to get the protection.
Then pay the balance off with the remaining part of the £5k before the due date, and hey presto !, no credit charges.
Remember, experience is proportional to the amount of money you have lost. Don't learn the hard way.
Afterthought: Even simpler would be to ring Barclaycard and ask for your credit limit to be raised to £5000. However, don't tell them its to get the protection of the Consumer Credit Act.