How to Make It
Bring the port to a boil in a medium-size heavy saucepan over medium-high heat. Lower the heat slightly and simmer until reduced to 1 cup (if using a gas stove, never let the flames extend above the bottom edge of the pan). Add the vinegar and simmer until almost reduced to a syrup, lowering the heat as necessary and watching carefully to keep it from burning around the edges—you should have about 7 tablespoons. (The sauce can be made to this point up to 1 week ahead; cover and refrigerate.)
Divide 1 tablespoon of corn oil between the skillets and place over high heat until just smoking. Divide the mushrooms, thyme and garlic between them and lower the heat to medium. Sauté until the mushrooms are browned, about 4 minutes. Turn the heat to low and add the shallot, salt, pepper and 2 tablespoons of the butter to the 2 skillets. Cook until the shallot is softened and the mushrooms are tender, about 6 minutes more. Discard the garlic and thyme and combine the mushrooms. (The mushrooms can be made to this point up to 1 day ahead; cover and refrigerate.)
Season the snapper on both sides with salt and pepper. Sprinkle the five-spice powder over the skin and rub it in. Clean the skillets and divide the remaining 2 tablespoons of corn oil between them. Place both over high heat until just smoking. Add the snapper to the skillets, skin side down, and briefly hold the fillets down with a spatula to prevent the skin from shrinking. Sauté until the bottom is dark and crusted, about 5 minutes. Turn and cook until a metal skewer inserted into the fish for 5 seconds is met with medium resistance and feels warm when touched to your lip, about 5 minutes longer. Keep warm.
Meanwhile, reheat the mushrooms. Bring the sauce to a boil over high heat. Cut the remaining 3 tablespoons of butter into 1/2 inch pieces. Lift the saucepan a few inches above the heat and add the butter. Shake the pan back and forth until the butter is melted and incorporated into the sauce; this will take about 3 minutes. Do not stir or whisk the butter into the sauce. When ready, the sauce will be very shiny and clear.
To serve, stir the chives into the mushrooms and arrange them in the center of 4 large plates. Top with the snapper. Drizzle the sauce around the mushrooms and serve immediately.