Warm the sesame oil in a wok over medium heat until fragrant.
Introduce the mung bean sprouts and sauté for approximately three minutes, allowing them to soften slightly.
Incorporate the mushrooms, pre-cooked chicken, bamboo shoots, green onions, and Chinese Five-Spice. Stir-fry everything together for about five minutes, or until the mixture is heated through. Take off the heat and set aside to cool.
Position an egg roll wrapper on a flat surface so it forms a diamond shape. Place roughly two tablespoons of the filling horizontally across the wrapper, about one-third of the way from the bottom, leaving a half-inch margin on each side.
Fold the bottom corner over the filling, then roll tightly once. Tuck in the side corners toward the center and continue rolling toward the top point. Dab a little egg wash on the final corner and press to seal the roll securely.
Heat about one inch of your chosen oil in a deep skillet or wok. Once the oil reaches frying temperature (a test egg roll should sizzle immediately), lower in four rolls at a time. Fry until the wrappers turn golden and develop bubbles on the surface.
Remove the cooked rolls and place on a plate lined with paper towels to drain any excess oil.
Serve hot alongside sweet and sour sauce.