There are 2 different issues.
1. For one child you can spend up to $5000 in FSA funds. That amount was pro tax so you saved $5,000 off of your income That is the maximum you can do.
2. Or you can claim child care credit with a maximum of $3,000 in expenses. Once you have used the $5,000 in expenses through the FSA you have already exceeded the $3,000 maximum for the child care credit and have no more expenses with which to claim that credit. You are better off with the FSA expense savings.
