Running This Adventure in 5e
So, when you port over Black Wyrm of Brandonsford, how do you do it? I'd probably start with a quick flowchart.
From there, there are two quests the PCs can try to resolve in town, one of which leads to Hogboon, and the other of which leads to the Witch. Another NPC points the PCs to the Giant's Hut. However the PCs are going about this, they need to have the information about the dragon up front, and as much other information as you can give them for the area (that the NPCs they talk to would know).
As to running a fight with the dragon, that's fairly simple. I'd grab the young green dragon statblock from the Monster Manual, and give it the traits described in the adventure. Notably, the scales are invulnerable, so regular attacks won't work unless you have magical weapons. The bite attack requires a DC 14 Con save, or it reduces the target's STR score by 1d6*. If the PCs don't have magical weapons, they can still make called shots at the eyes or mouth with disadvantage.
The book lists two broad ways the PCs can overcome the dragon - either by getting the magical dragon-slaying sword of Sir Brandon from the titular gentleman's tomb, or by drugging it with the treewine from the Faun's Grove and delivering the dragon to Hogboon. Hogboon will then turn the dragon on the village, and wipe it out (although he doesn't tell the PCs that).
It is notable that these are just the surface. Your players could bury it in a landslide (it still needs to breathe, so smothering the dragon kills it), drug it and then kill it by climbing into its mouth and stabbing it in the brain, piss it off and lead it to Hogboon so it wipes out the goblins, etc. You don't need to plan for every eventuality; you just need to know the NPCs, their abilities, and their desires. From there, it's all down to what the players bring to the table.
Alright, y'all! I'm off to do battle with shrubbery! But next time, we'll talk about converting OSR-style mechanics to 5E!
*Ingrid or the Witch can help you recover this ability score damage for 250 gp per point.
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