The only reason to enter the foreign income in the foreign tax credit section is it may increase your foreign tax credit. But if it is only $5 there is no reason to bother with it. Applying for the foreign tax credit is optional, so you don't need to report the minimal income amount in that section. It would only be reflected on the Form 1040-X if your foreign tax credit increased.
You don't need to file the amended return for the state with a refund if you don't want to bother with it, only if your tax increased. The state returns are not inter-related as far as the taxing authorities are concerned, so it won't matter if you file certain amended returns and not others.
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