Cut the pork into thin slices; cut each slice into slivers about 1/4 inch wide.
Pull off and discard the stems of the shiitake mushrooms. Thinly slice the caps.
Cut off and discard the tough sections of the wood ear mushrooms. Thinly slice the wood ears.
Peel and mince the garlic.
Peel and grate the ginger.
Chop the chili.
Peel and julienne the carrot (note that bamboo shoot is the traditional vegetable for hot and sour soup, but I like carrot better).
Cut the soft tofu into half-inch cubes.
Heat the cooking oil in a pot.
Saute the ginger, garlic and chili with the five-spice powder in the hot oil until lightly browned.
Add the pork to the pot and cook until lightly browned.
Add the shiitake to the pork.
Pour in 7 cups of broth and soy sauce. Stir in the sugar. Bring to the boil. Lower the heat, cover the pot and simmer for 10 minutes.
Disperse the corn starch in the remaining broth and pour into the pot. Stir until the broth is thick and clear.
Add the tofu cubes, wood ears and julienned carrot to the soup. Bring to the boil and simmer for 5 minutes
Turn off the heat and stir in the black vinegar. Taste. Add more salt if necessary (adding more soy sauce will make the soup too dark).
Garnish the hot and sour soup with scallions and serve at once.