Get your taxes done using TurboTax

You asked, 

"Why $5361.90 is included as income and taxable while this is an amount that church pays for the day care. Its a discount because my wife is their employee. $10361.90 are expenses for the day care that church pays as discount.  "

The IRS says (note that "you" refers to your employer, not you personally):

"Box 10—Dependent care benefits (not applicable to Forms W-2AS, W-2CM, W-2GU, or W-2VI). Show the total dependent care benefits under a dependent care assistance program (section 129) paid or incurred by you for your employee. Include the fair market value (FMV) of care in a daycare facility provided or sponsored by you for your employee and amounts paid or incurred for dependent care assistance in a section 125 (cafeteria) plan. Report all amounts paid or incurred (regardless of any employee forfeitures), including those in excess of the $5,000 exclusion. This may include (a) the FMV of benefits provided in kind by the employer, (b) an amount paid directly to a daycare facility by the employer or reimbursed to the employee to subsidize the benefit, or (c) benefits from the pre-tax contributions made by the employee under a section 125 dependent care flexible spending account. Include any amounts over $5,000 in boxes 1, 3, and 5"

See IRS Instructions for line 10 for the W-2.

The church is following the IRS instructions for the W-2. Essentially, the church is not allowed to give you child care benefits in excess of $5,000 that are tax free. Thus the $5,361.90 in excess of the $5,000 limit is reported as taxable income.

When in the child and dependent care interview you are asked about how much you spent on your child, answer with $3,500. Don't include the amount that the

church kicked in in box 10 on the W-2.

When you are asked how much your child care provider was paid, answer with $10,361.90+$3,500 ($13,861.90 if my math is correct). When you are asked how much was left over in your FSA, answer 0 (if that's true - I assume that the church took every penny). 

At the end, TurboTax should tell you that you have received $0 for the credit, which would be correct.

You tax benefit is that the church paid for the first $5,000 of the child care and excluded this amount from your income (so you didn't pay any tax on that $5,000).