For US purposes you are taxed on world-wide income so you are required to report the sale of the Panama property. On your Federal income tax return you will then be able to claim a foreign tax credit (Form 1116) for the Panamanian taxes already incurred. So if the US tax is 20% and you already paid 5% to Panama then you would pay the additional 15% due on your US tax return.
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As a general rule, permanent residents (aka Green Card holders) are treated the same as US citizens for federal income tax purposes -- which means you are generally taxed on your world-wide income. Whether you purchased the property prior to becoming a US permanent resident may not matter for US tax purposes since you are selling the property now (when you are a US permanent resident). The amount of US tax on the sale of the property in Panama and the availability of a US tax credit for Panama tax paid on the sale depends on a number of facts and circumstances not described in your fact pattern. Please contact a tax advisor for a more specific answer to your issue.
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