FSA/Child and Dependent Care Credit Question?

Can you clarify this FSA/Child and Dependent Care Credit question for me?  Married Filing Jointly, 2 Children, Child #1- $9068 in childcare expenses, Child #2 - $6996 in expenses.  Total - $16064.  We funded my wife's FSA with $5000.  Is it true that this only allows us to claim the remaining $1000 under the Child and Dependent Care Credit?  I would think we could claim the entire $6000 since we spent more than that over and above the $5000 we put into the FSA.  The FSA was not funded by the employer.