Cards are tied to individual accounts. I don't think there is any way to access a different account just because it is in the same bank.
You are going to be stuck with fees. I would get what you need with the credit card. Assuming you are set up for online banking, immediately pay off the amount you took, plus the fees, plus your normal minimum payment, plus a little more to be safe. Banks are required to apply payments above the minimum to the highest interest balance. That will at least stop interest from accruing within a day or two, but you are likely stuck with the 5% fee.
Also check to see if you can get cash from a bank teller with the card for lower fees. I think all of the ones I have read are basically the same as the ATM, but there could be a difference.