Your child tax credit is $0, because you have no tax liability (with $10K of income).
Your Additional Child Tax Credit (refundable ) is ($10,000 - 2500) x 15% = $1125. This is calculated on form 8812. The 5 x 2000 = 10,000, you see on Schedule 8812 is just the starting point of the calculation.
The Earned Income Credit is only up to 3 children. For $10K it will be around $4500
