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If your score is close to 700, you might want to consider the Discover it® Cash Back. The card comes with 15 months of 0% intro APR on balance transfers (17.49% - 26.49% Variable APR after that). There is a 3% intro balance transfer fee (equivalent to $150 for a $5,000 transfer), then up to 5% on future balance transfers. This card also comes with cash back rewards and no annual fee, so you may want to keep it after you pay off your debt.

After transferring your balance to a new card, your total debt will be around $5,000 plus a fee of $150, so your monthly payment should be at least $344 if you want to pay off your debt without accruing interest and provided that you do not have any additional expenses on the card.

The transfer process may take anywhere from a few business days to a few weeks for new card accounts. That means you may have to make another monthly or regular payments on that old debt you're trying to move.

If you keep your old cards open, you will also need to make regular payments, like annual fees, on these cards. Otherwise, you can simply close your old accounts, but it will have an impact on your credit history and score.

If your score is lower, you might want to consider personal loans. You can choose the duration of the loan and request a specific amount (or a little more). The amount of the loan and interest rates are negotiable, while it depends on the bank which credit limit will be approved for a credit card.

A personal loan is a common alternative to a balance transfer card. If you get a personal loan, you can use that to pay off your debt and then make payments on the loan.