In a large, nonreactive bowl, toss the chicken with five-spice powder, then with the juice of 2 of the limes, the soy sauce and the ginger. Cover and marinate in the refrigerator for at least 30 minutes and up to 6 hours.
Heat oils in a large skillet over medium-high heat. There should be at least 1/4 inch of oil in the pan. When the oil is hot, remove chicken from marinade, allowing excess marinade to drip back into the bowl, and fry, in batches if necessary to not crowd the pan, turning the pieces frequently, until well browned and cooked through, 15 to 20 minutes.
Meanwhile, make the dipping sauce. Combine oyster sauce, a tablespoon of the Scotch-bonnet-pepper sauce and the juice of the remaining lime and stir to combine. Adjust seasonings with more hot sauce, lime juice and freshly ground black pepper to taste.
Garnish with scallions and serve with white or fried rice, with a drizzle of the sauce over each piece of chicken and the remaining sauce on the side.