Heat oil in a skillet over medium-high and cook onion until soft, about 3 minutes. Add garlic and five-spice; stir 30 seconds.
Add minced chicken and cook, breaking it up, until no longer pink, about 6–8 minutes.
Stir in soy, hoisin, rice vinegar, and shredded veggies; cook 2–3 minutes until veggies soften but keep some crunch.
Whisk peanut sauce ingredients in a small bowl, adding water to reach drizzling consistency.
Spoon chicken mixture into lettuce leaves, drizzle with peanut sauce, and top with green onion and cilantro.