When married filing separately, you can't clam the credit, but you can use an FSA of $2500 (half the amount for married filing jointly.) But, the child must be your dependent, or must live with you more than half the year and be listed on your tax return as a qualifying person.
So if your child is not a dependent, you don't get anything and the entire $5000 is added back to your taxable income,
If you can list your child as a qualifying person, you can use $2500 as a non-taxable benefit and the other $2500 gets added to your taxable income. But, you may not be able to claim the child as a qualifying person.
What are your living and custody circumstances?
