Lancelot
Adventurer
About a dozen dragon fights in 5e, but my group plays frequently (1.5 sessions per week, averaging 5 hours each). To answer your questions...
Circumstances vary, but I've listed some examples below. The fight is always tough, because I play most dragons as smart. They take out weakened characters first, the go for maximal area coverage with their breath weapons, they take to the air if the party is relying on melee damage, they will coup de grace a fallen opponent if he/she has "got up" after being dropped at least once (e.g. they were healed, or have some form of regeneration).
The single most feared tactic I use is the Legendary action beatdown. The dragon observes the first round of combat, and sees who is going "last" in the turn. Let's call that person PC#4. On its second turn (and thereafter), the dragon flies next to that person and drops a full claw/claw/bite attack. It is now PC#1's initiative. They take their turn. Unless the dragon is somehow pushed away or otherwise inconvenienced, it uses a legendary action at the end of PC#1's turn to bite PC#4. And the same at the end of PC#2's turn. And the same at the end of PC#3's turn. By the time PC#4's turn starts, they will have weathered 4 bite attacks and 2 claw attacks. That's usually a problem for any character, especially the primary party healer.
Other useful tactics include full attack on a melee PC acting late in the initiative order, then Legendary action to bite on PC#1's turn, then Legendary action to wing blast and move out of range on PC#2's turn. Melee PC#4 has just taken a bunch of damage and now cannot get close enough to retaliate. For breath weapons, the dragon will obviously target conscious foes... but I never hesitate to include unconscious PCs in the area if I can. That extra death box (from taking damage while unconscious) can add a lot of tension.
Perhaps unsurprisingly, dragons are the leading source of character deaths in our group. I wouldn't play them like this if I was DMing for kids. But here's the deal: my players are experienced, they're okay with high casualty rates, and they have full knowledge that dragons are going to be their deadliest foes. In most cases, they don't need to engage them - it's their choice, because they know the rewards. They also relish the sense of excitement knowing that a dragon will always represent the ultimate challenge.
On to the Adventure Path examples...
1) The white dragon at the end of HotDQ was a TPK. The telling factors were lair actions, legendary actions, and enough room to move around and take flight. This is always a problem for parties. If the dragon can make full use of its movement (even if it provokes a single attack when moving away), it wrecks certain character classes: barbarians, monks, paladins, some fighters, some clerics, etc. Many of these classes rely on melee damage. In this case, I was taking full advantage of the old "full attack, legendary bite, legendary wing blast and move back out of melee range" strategy.
2) Iymrith, at the end of SKT, was a TPK... but it was a near thing. The party was buffed up with giant potions and had four storm giant allies... but I was playing Iymrith absolutely optimally. A DC 23 breath weapon was virtually an auto-fail for the PCs, which means they were losing 90HP every breath (and I was lining the breath to get maximal coverage). The two party healers were priorities, and they were rather low on spells anyway after dealing with a horde of the dragon's servants (gargoyles and suchlike) earlier. The beauty of the breath weapon is around action economy. If the dragon can drop 2 PCs in a single action, the surviving PCs usually have to burn their actions on healing to get their buddies back into the fray. This ruins the entire party's round. This happened a couple times in a row, and the group simply ran out of gas. One character was particularly annoying in that he had a regenerative power (regain HP at start of turn if still alive), so Iymrith dropped next to him and knocked him unconscious with the ol' claw/claw/bite. On PC#1's turn, the dragon dropped a legendary bite on the fallen PC#3 (auto-crit; 2 death boxes)... and then finished him off on PC#2's turn. No regeneration.
3) The adult red dragon in Wyrmtooth Mine (ToA) was a TPK. Usual tactics, although this one was a little more cinematic. The party was riding an out-of-control mine cart. When they saw the dragon up ahead, they intentionally jumped the tracks and slammed the cart into its head. Their problem, however, was that they had already burned a bunch of resources fighting kobolds earlier in the mine. Kobolds, you say? What challenge could they possibly be? The issue was that they had no area-effect spells in the party, and there were dozens of the little guys. Even higher-level adventurers need to worry about accumulated damage, thanks to kobold pack tactics (advantage on attacks if adjacent ally). Also, the kobold fight created enough racket that the dragon was aware of intrusion in it's lair and was never going to give the party an hour to short rest. So, they only had a few rounds to burn healing spell slots (rather than recover HP via hit dice) before it was all on with the dragon.
4) The dragon turtle in PotA was not a TPK. In fact, it was a huge disappointment. It lost initiative and received a hypnotic pattern. This incapacitated it. The party moved forward and readied actions to all strike at the same moment on the incapacitated beast. A huge round of auto-crits ensued, and the beast was dead a round later. Shame. Legendary Resistance is a game-changer, and unfortunately dragon turtles don't have it.
5) ...but the red dragon that showed up later in PotA made up for it. It wasn't a TPK, but the party had to flee. The single most dangerous PC in the group was a bear totem barbarian, who handled most encounters by tanking for the party. Thanks to healing support and 1/2 damage from all non-psychic, he could take literally hundreds of HP's of damage before dropping. So... the dragon simply refused to engage. The barbarian raged in the first round; the dragon breathed on every other PC, then simply flew away. The barbarian took no damage and wasn't in range to attack - his rage ended the next round (and note: I don't permit shenanigans such as allowing the barbarian or his allies to damage himself for a few points to keep his rage going). The dragon flew back and wrecked the party for a round. The barbarian burned another rage... and the dragon retreated again. The players rapidly figured out that they couldn't rely on the barbarian to soak, and decided discretion was the better part of valor. Wise choice.
Circumstances vary, but I've listed some examples below. The fight is always tough, because I play most dragons as smart. They take out weakened characters first, the go for maximal area coverage with their breath weapons, they take to the air if the party is relying on melee damage, they will coup de grace a fallen opponent if he/she has "got up" after being dropped at least once (e.g. they were healed, or have some form of regeneration).
The single most feared tactic I use is the Legendary action beatdown. The dragon observes the first round of combat, and sees who is going "last" in the turn. Let's call that person PC#4. On its second turn (and thereafter), the dragon flies next to that person and drops a full claw/claw/bite attack. It is now PC#1's initiative. They take their turn. Unless the dragon is somehow pushed away or otherwise inconvenienced, it uses a legendary action at the end of PC#1's turn to bite PC#4. And the same at the end of PC#2's turn. And the same at the end of PC#3's turn. By the time PC#4's turn starts, they will have weathered 4 bite attacks and 2 claw attacks. That's usually a problem for any character, especially the primary party healer.
Other useful tactics include full attack on a melee PC acting late in the initiative order, then Legendary action to bite on PC#1's turn, then Legendary action to wing blast and move out of range on PC#2's turn. Melee PC#4 has just taken a bunch of damage and now cannot get close enough to retaliate. For breath weapons, the dragon will obviously target conscious foes... but I never hesitate to include unconscious PCs in the area if I can. That extra death box (from taking damage while unconscious) can add a lot of tension.
Perhaps unsurprisingly, dragons are the leading source of character deaths in our group. I wouldn't play them like this if I was DMing for kids. But here's the deal: my players are experienced, they're okay with high casualty rates, and they have full knowledge that dragons are going to be their deadliest foes. In most cases, they don't need to engage them - it's their choice, because they know the rewards. They also relish the sense of excitement knowing that a dragon will always represent the ultimate challenge.
On to the Adventure Path examples...
1) The white dragon at the end of HotDQ was a TPK. The telling factors were lair actions, legendary actions, and enough room to move around and take flight. This is always a problem for parties. If the dragon can make full use of its movement (even if it provokes a single attack when moving away), it wrecks certain character classes: barbarians, monks, paladins, some fighters, some clerics, etc. Many of these classes rely on melee damage. In this case, I was taking full advantage of the old "full attack, legendary bite, legendary wing blast and move back out of melee range" strategy.
2) Iymrith, at the end of SKT, was a TPK... but it was a near thing. The party was buffed up with giant potions and had four storm giant allies... but I was playing Iymrith absolutely optimally. A DC 23 breath weapon was virtually an auto-fail for the PCs, which means they were losing 90HP every breath (and I was lining the breath to get maximal coverage). The two party healers were priorities, and they were rather low on spells anyway after dealing with a horde of the dragon's servants (gargoyles and suchlike) earlier. The beauty of the breath weapon is around action economy. If the dragon can drop 2 PCs in a single action, the surviving PCs usually have to burn their actions on healing to get their buddies back into the fray. This ruins the entire party's round. This happened a couple times in a row, and the group simply ran out of gas. One character was particularly annoying in that he had a regenerative power (regain HP at start of turn if still alive), so Iymrith dropped next to him and knocked him unconscious with the ol' claw/claw/bite. On PC#1's turn, the dragon dropped a legendary bite on the fallen PC#3 (auto-crit; 2 death boxes)... and then finished him off on PC#2's turn. No regeneration.
3) The adult red dragon in Wyrmtooth Mine (ToA) was a TPK. Usual tactics, although this one was a little more cinematic. The party was riding an out-of-control mine cart. When they saw the dragon up ahead, they intentionally jumped the tracks and slammed the cart into its head. Their problem, however, was that they had already burned a bunch of resources fighting kobolds earlier in the mine. Kobolds, you say? What challenge could they possibly be? The issue was that they had no area-effect spells in the party, and there were dozens of the little guys. Even higher-level adventurers need to worry about accumulated damage, thanks to kobold pack tactics (advantage on attacks if adjacent ally). Also, the kobold fight created enough racket that the dragon was aware of intrusion in it's lair and was never going to give the party an hour to short rest. So, they only had a few rounds to burn healing spell slots (rather than recover HP via hit dice) before it was all on with the dragon.
4) The dragon turtle in PotA was not a TPK. In fact, it was a huge disappointment. It lost initiative and received a hypnotic pattern. This incapacitated it. The party moved forward and readied actions to all strike at the same moment on the incapacitated beast. A huge round of auto-crits ensued, and the beast was dead a round later. Shame. Legendary Resistance is a game-changer, and unfortunately dragon turtles don't have it.
5) ...but the red dragon that showed up later in PotA made up for it. It wasn't a TPK, but the party had to flee. The single most dangerous PC in the group was a bear totem barbarian, who handled most encounters by tanking for the party. Thanks to healing support and 1/2 damage from all non-psychic, he could take literally hundreds of HP's of damage before dropping. So... the dragon simply refused to engage. The barbarian raged in the first round; the dragon breathed on every other PC, then simply flew away. The barbarian took no damage and wasn't in range to attack - his rage ended the next round (and note: I don't permit shenanigans such as allowing the barbarian or his allies to damage himself for a few points to keep his rage going). The dragon flew back and wrecked the party for a round. The barbarian burned another rage... and the dragon retreated again. The players rapidly figured out that they couldn't rely on the barbarian to soak, and decided discretion was the better part of valor. Wise choice.