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So when they send me a BT check, can I just deposit it into my bank account, and pay off my 5 cards electronically? Or do I have to write out the checks to the 5 cc companies and send in the mail?
^Write yourself a check.
You'll usually get BT checks. These are not cash advances. They have a promotional APR for a specified period of time (usually 12, 18, 24 months).
Make sure the BT fee is 1% or less. I never BT unless I get 1% or less BT fee with 0% APR for no less than 18 months. That's considered a prime BT offer. Everything else is BS.
Once you drop it into your bank, it's cash money, then you do with it as you please.