The Child Tax Credit is completely different than the Dependent and Child Care Credit. You are correct that you are not eligible for the Child and Dependent Care Credit since you maxed out with your $5,000 deferral to your Dependent FSA. However, this does not affect your ability to claim the Child Tax Credit of $2,000 for your child.
For more information, check out the TurboTax FAQ below:
https://ttlc.intuit.com/replies/3301702
