Stop using the card to charge things, but you MUST pay the bill every month.

Lets sum this up.

1) When you use a credit card you are borrowing money from the credit card company. You are required to pay that money back with interest.
2) You receive a monthly statement telling you what the previous balance was, how much was charged during the month (if any), how much you paid during the month, how much interest was charged for that month on the outstanding balance and what the new balance is. The statement also tells you your annual APR (usually different amounts for purchases and cash advances) and also the daily rate on the outstanding balance.
3) By law they have to tell you how long it will take to pay off the balance if you just pay the minimum payment.
4) The monthly interest is added to your balance and then additional interest is charged on that. On a $5000+ balance your monthly interest is likely to be $89+ and if you don't pay at least the interest, your balance will continue to rise.
5) Closing the account will not change this. All closing the account will do is prevent you from using the card to purchase more. The interest will continue to to be charged and compound.

I suggest you contact a credit counseling service to negotiate with the card issuer on your behalf.