Mix soy sauce, oil, five-spice powder, and sugar in a shallow dish. Turn chicken in marinade and let stand 5 to 10 minutes.
Heat a large pot of water to boiling.
Drain chicken, discarding marinade. Oil cooking grate, using tongs and a wad of oiled paper towels. Grill chicken, covered, turning once, until cooked through, 10 to 12 minutes. Transfer to a cutting board and let rest 5 minutes.
Add vermicelli to pot of water and turn off heat. Let stand until soft, 5 to 10 minutes; drain.
Divide noodles among dinner bowls. Thickly slice chicken, set on noodles, and top with carrots, herbs, and peanuts. Serve with dressing.