Q. Do I amend my return to get the $500 credit for the other 2 kids?

A. No. You are already covered for the 5 x $500 child stimulus payment, if the 5 kids are listed as dependents on the form 1040.

Although the EIC calculation is limited to three kids, you still get the child tax credit on all kids under 17 (up to the limits). You get a $500, non refundable, dependent credit (separate for the stimulus $500) for each child over 16.

The child tax credit  (CTC) is also limited to your tax liability. The CTC is a non-refundable credit and can only reduce your income tax to 0, It can not help you beyond eliminating your tax liability. But, if you have more than $2500 of earned income, some or all of it is usually given back to you thru the "Additional Child tax credit". That is, part of the CTC may be on line 18b of form 1040 (2019 version) instead of line 13a (lines 17 and 12 in 2018).   The  ACTC is calculated on form 8812 and  is basically 15% of your earned income over $2500. The ACTC is a maximum of $1400 per child (not $2000).

But even if your income limits the amount of CTC and ACTC that you get, you will still get the $500 stimulus check for each kid who was under 17 on 12-31-19.