There are questions online about whether Mongolian horse archers could hit a target accurately over 500 meters with effectiveness. However, we have to be mindful about how history and recounts of one’s tales usually are over-exaggerated.
In truth Mongolian recurve bows are most effective at around ~100 meters range, and anything further than that, archers had to use special types of arrows that are light and bows with significantly heavier draw weights.
Why ~100 meters is the most effective?
If you look at English longbows, a typical war bow draw weight ranges from 80lbs to 150 lbs. Heavy draw weight longbows can shoot a bit over 300 meters, but typical archers in the medieval period used the longbow most effectively at distances less than 200 meters, but the closer they are to their target, the more penetrative power they had.
The Mongolian bow does rival the English longbow when it comes to how far it could shoot, but the arrow that was used by Mongolian warriors didn’t have the same penetration power as English longbows. It’s almost impossible for an arrow shot from a Mongolian bow to penetrate plate armor head-on.
Hence Mongolians most often used Parthian tactics by getting in close and feigning a retreat whilst shooting arrows. The main goal was not to necessarily penetrate armor but to hit between the gaps of armor and cause disarray in their enemies.
The Absolute Farthest a Mongolian Bow Could Shoot
If you are talking about shooting an arrow as far as possible disregarding effectiveness and penetration power, then shooting more than 300 meters, and even up to 500 meters is possible.
Ivar Malde set the world record for the farthest distance shot with an all-natural Turkish-style bow at 566 meters, so it is most likely that Mongolian archers in medieval times did shoot as far since Turkish and Mongolian bows are rather similar in build and construction.