We are married but filling separately. I contributed $5,000 to a DC FSA; he did not contribute anything. The full $5,000 was spent. Did I/we exceed the IRS limit?

I know that the IRS limit for a dependent care FSA is $5,000 if married filing jointly, or $2,500 per person for married filing separately. We only have one Dependent Care FSA, but only I contribute to it. Did we exceed a limit and/or would we owe taxes on the other half of the $5,000?