If your card has a 5K balance at 19 percent and they approve a second card for a 5K cash advance at 3.9 can you use it to pay off the first card?

Most credit card companies will not allow you to pay one debt off for another, and for obvious reasons in this case (it would reduce your APR from 19 to 3.9). However, this doesn't mean you can't shop around for a card somewhere else to pay it off. 19% is fairly high so I would definitely suggest looking elsewhere to transfer the balance.

You can do what you want with cards from separate companies, but usally not with cards from the same company. However, there is a simpler way to solve this problem.

Many credit card companies will reduce your interest rate if you just call and ask for the rate to be reduced (assuming that you are current with your payments.) Last year I had my interest rate reduced from 18% to 5%, just by making a 3 minute phone call. The industry is very competitive and they want to keep your business.