It looks like no, not if they are carnivores, but it is possible if they are omnivores
There is a nice helpful calculator for this.
So if your dragons metabolism is comparable to a dinosaur or mammal you are looking at roughly about 1,039,878 kilocalories a day, per dragon.
With 975 kilocalories for a pound of beef, that is ~1067 lbs of beef, or roughly
1,778 lbs of cow (only about 3/5th of a cow's weight is "food" aka not bone or skin).
A medieval cow weighed about 75% of a modern cow and a modern cow weighs on average 1,390lbs (so medieval would be 1,045lbs). So that is roughly 2 cows per day per beast or 730 cows per year per beast.
Now what does this mean for your kingdom
It takes 1.5 to 2 acres to feed a cow/calf pair for 12
months and takes about 2 years to raise a cow to slaughtering age, **so to feed your beasts for 1 year, you need 1460 acres of pasture That is roughly 1 large barony (of half one on the small estimate) just devoted to feeding one animal.
For 500 dragons we are looking at 730,000 acres)
Now England contained roughly 43 million acres of farmland today, so it is indeed possible, but you would be looking at 1.6% of the total farm land, and that is modern farmland, BUT a lot less would have been farmable during medieval times, medieval england only had approximately 8,000,000 acres of farmland (according to the domesday survey) that would mean you are using 9% of your total farmland. This is where the estimate gets a bit sketchy pastureland is not the same as farmland but at the same time the medieval farming systems were only capable of utilizing about half the farm land at any given time. Either way thats a huge amount of food, probably more than they could spare. (estimates are medieval communities could only spare about 2% of their food production for the military.
So in the end you might well be be starving your farmers to feed the dragons. At the very least would have very little else including no other military or aristocracy, which means their country would very quickly fall apart because it can't feed it's own government.
EDIT alternatively if you go with Will's idea and say they are herbivores (or omnivores) you are looking at only ~200,000 acres to feed all of them, that much more reasonable, double the acreage and say they get some meat/fish with each meal and you have something with a noticeable impact on the kingdom but not a prohibitive one.