If you have 1 qualifying child, you have gotten the most benefit that is possible with a $5000 pre-tax FSA. Keep in mind that having an FSA for $5000 is usually better than having a credit based on $3000 in expenses. That $5000 in deferred income never touches your tax return.

The reason you have to enter your expenses into your return is because you need to verify with the IRS that your FSA account was used for actual qualifying expenses. Entering more than the FSA isn't going to do anything for you.

The Dependent Care Credit is limited to $3000 in expenses per child. If you have an FSA, your limit is actually raised to $5000 for one or more children. You could only get an extra credit on your tax return if your FSA was under $3000. If you had 2 children, and your FSA was $5000, you can get a credit for that extra $1000.

But, under no circumstances can you max out an FSA and get a credit on your return for one child. That is simply the law.

Per @ChristinaS

Thanks for your help!

How does it work with a dependent care FSA, does it roll over from year to year?

If I put $5,000 , but I only use $4,000 , can I use the extra $1,000 in 2021?

No. Amounts not used are forfeited. 

Internal Revenue Service (IRS) rules provide an employer two options for unused health care flexible spending account (FSA) funds. Previously, employers had to follow the "use it or lose it" rule, meaning that any account balances left at the end of the year were forfeited. An employer must still follow the "use it or lose it" rule for dependent care FSA funds. A dependent care FSA plan allows for a reasonable time for employees to submit claims after the plan year-end, but all dependent care expenses must be incurred by plan year-end.

FSA