The 5e DMG describes the tiers of the game from levels 1-4, where you fight rats in a basement, to level 17-20, where you fight "wyrms of tremendous power, whose sleep troubles kingdoms and whose waking threatens existence itself."
Wow, that's some high flown rhetoric about dragons! Let's take it seriously and see where it takes us.
First of all, sleep and waking are traditionally very important to dragons. In old school d&d, dragons are, I think, the only monsters with a chance to be asleep when discovered in their lairs. This is clearly an emulation of Smaug, who is asleep when Bilbo finds him and who has been holed up in his lair, apparently, for about sixty years. So dragons hibernate. Like cicadas, they have an active period when they desolate the countryside and a sleeping period of 30+ years when they leave their nests little if at all. I propose that the older the dragon, the longer the sleeping period. The d&d world just can't support lots of existence-troubling dragons all awake at once.
Their sleep troubles kingdoms. What does that even mean? The simplest and most boring explanation is that everyone is worried about when the dragon will wake up. Possible, but not mythic enough. Another possibility: those world-altering 5e "lair effects" persist during the dragon's hibernation. Undoubtedly true, but the area around a dragon's lair is probably wilderness anyway. I don't see lair effects troubling kingdoms. The best explanation I have is that hibernating dragons aren't 100% asleep. They can wake or semi-wake for brief periods, maybe even lash out a casual claw to wipe out a foolish lair intruder. And they can have conversations. They can get reports from their spies, bandy words with bold explorers, and send kobolds to negotiate alliances with other evil monsters. The diplomacy and threats of an ancient dragon could trouble nations, and perhaps truly powerful dragons can use other powers from far away. Green to twist the minds of mortals. Black to bring eclipses and darkness. Red to spark rage-fueled wars and wildfires. Et cetera.
Of course, if anyone seriously angers a hibernating dragon by wounding it or by stealing its treasure, it will fully wake and start its ravages early. So the countryside will try to persuade the adventurers: "Let sleeping dragons lie."
Waking threatens existence. That seems like that's gotta be hyperbole, right? They're just dragons. Sure, dragons have good stats, and an ancient dragon could probably torch a palace and decapitate a kingdom or two, unless the kingdom has some epic level heroes handy. But existence? Like, the whole material plane and the other planes as well?
Ok here is my theory. There are only a literal handful of dragons who can actually raise this sort of existential threat: one of each chromatic color, in fact. Here I am taking a cue from Rory's game world. He has an important NPC black dragon who is an oracle to those brave enough to visit its lair (if it conforms with my house rules proposed above, it is in its hibernation period and is probably using its oracular power for some sinister future purpose). As far as Rory has revealed, this is the most powerful black dragon in the world, but it doesn't necessarily attack its visitors. But imagine the devastation that this infallible black dragon will wreak when it wakes up. Let's say that, likewise, the master of green dragons has a charmed coterie of spies in every palace and its claw on the domino which could topple civilization. The white dragon master is not cunning like its peers: it is simply cold personified. Packs of winter wolves coalesce from its icy snores. When it wakes, it wreaks ice-age blizzards in which glaciers roll towards the heart of the world. Blue and red dragons: I can't think of the powers of the two strongest dragons right now. Perhaps you can. If so, leave a comment. The point is, each dragon has the individual power to threaten kingdoms or the world, though not existence itself. But here is the thing. These five master dragons are on sleep cycles from, say, 28 years for white to, say, 60 for red. If they are ever all awake at once, they, Voltron-like, form an unchained Tiamat. And then existence really is threatened.