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Thge Iron Hills was the most capable country in the North to stand in the way of Sauron at the time of the Hobbit, so I calculated that if the 500 that were at the Battle of Five Armies was just around five-ten percent of Dain's army then it would be around 5-10,000. So in a sense it is logical number.
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Just because it was "most" capable doesn't equal "very" capable.
I am also a little puzzled by that remark by Gandalf because it ignores the Woodland Realm which was also in the area and had more soldiers at the Battle of Five Armies, but perhaps they would have been taken up by Dol Guldur, but that is a discussion for another time.
I have a problem with the arbitrary decision that the 500 dwarves was just 5-10% of Dain's army. Why do you think that? I think Dain would have brought every dwarf he could spare because of the critical nature of the enterprise. While I agree that perhaps Dain did not bring along every dwarf of his who could bear arms, I think he would have brought the vast majority of them.
To the best of my understanding the Iron Hills had never been much more than an outpost. If it had been more than that, why wouldn't the Kings of Durin's Folk have relocated there after the Lonely Mountain fell? I think Dain brought few dwarves because he had few to bring.
Also, the dwarves were never a numerous people when compared to Men and orcs, especially during this time of their decline.