Mix hoisin sauce, rice vinegar, garlic, oyster sauce, soy sauce, toasted sesame oil, and Chinese five-spice powder together in a bowl. Add chicken strips and let marinate for 10 minutes.

Heat 1 tablespoon sesame oil in a large wok over medium-high heat. Add marinated chicken. Stir-fry until no longer pink in the center and juices run clear, about 5 minutes. Transfer chicken to a bowl. Wipe out wok.

Pour remaining tablespoon sesame oil into wok over medium-high heat. Add shiitake mushrooms, napa cabbage, carrots, red cabbage, and scallions; stir-fry until crisp-tender, about 3 minutes. Pour in water.

Pour beaten egg into vegetable mixture; stir-fry 1 to 2 minutes. Add cooked chicken and stir-fry to combine.

Heat pancakes according in a microwave oven until warmed, 30 seconds to 1 minute.

Divide stir-fry mixture between pancakes and fold over like a taco or wrap like a sandwich wrap. Serve.