the dependent care credit is not $6,000. that amount is the maximum amount of expenses that qualify.
without an FSA, a maximum of $6,000 of expenses would qualify. the credit ranges from 20% to 35% of these expenses based in AGI (adjusted gross income). you can review for 2441 to see what rate you qualify for. (line 8 on the form) https://www.irs.gov/pub/irs-pdf/f2441.pdf
with an FSA, your taxable wages would be reduce by $5,000 . this $5,000 would reduce your maximum qualifying expenses to $1,000. again the credit rate applied would be based on you r AGI
by the way both you and your spouse need earned income to qualify for the dependent care credit. and if their earned income is lower than either the other spouse or the qualifying expenses that's what used to calculate the credit. it is even possible that if one spouse has little earned income part or all of what went in to the FSA would be taxable
