How can I qualify for EB-5 if my passport is expired?

I think you may be referring to an E-2 treaty investor. The answer is to apply to renew your Armenian passport. The E-2 visa has to be applied for abroad unless you are seeking E-2 status which would have required you to enter on the Armenian passport.

I have not heard of any nationalities being prohibited from the EB-5 program (You may be thinking about E-2.)

You can apply for EB-5 from any country. Are you willing to invest $900,000 for EB-5? Or are you talking about E-2 for a smaller investment?

I do not think EB-5 has limitation on origins. You may have mistaken it for E-2.

I do not see why you cannot apply for EB-5 based on being a Dominican citizen. You can also apply for EB-5 even though Armenian passport expired as long as you are in lawful status in the U.S. I would apply to renew if you can.

EB-5 is not limited to any specific country, unlike the E-2 nonimmigrant treaty investor visa, which requires a treaty country nationality. Therefore, you could apply for EB-5 using your Dominican Republic passport. Or you could renew your Armenian passport, if eligible.

To get an immigrant visa, inside the U.S. through adjustment of status, one must be in legal, nonimmigrant status. Whether or not the passport is expired.