Heat 1 tablespoon olive oil in a large pot or Dutch oven over medium-high heat until shimmering. Add 1 1/2 cups sliced celery and 1/2 cup diced onion and cook, stirring occasionally, until softened, about 3 minutes.
Add 2 teaspoons minced fresh garlic and 1 teaspoon minced fresh ginger and cook, stirring, until fragrant, about 1 minute.
Add 1 1/2 cups sliced carrots and cook, stirring, for 2 minutes.
Pour in 6 cups reduced-sodium chicken broth and add 3 tablespoons fish sauce. Add 2 stalks lemongrass (each cut into three pieces). Place the 6 star anise pods in one tea ball or spice infuser and the black peppercorns in another, and add both to the pot.
Pat 1 pound chicken thighs dry, rub them thoroughly with 1 tablespoon Chinese five-spice, and add the thighs to the pot so they are submerged in the broth.
Increase heat to high and bring the pot to a boil; boil for 3 minutes. Reduce heat to maintain a steady simmer, cover, and simmer for 30–45 minutes (30 minutes is sufficient; 45 minutes yields more flavor).
While the soup simmers, cook 5 ounces rice noodles according to the package directions, drain, and set aside.
Use a slotted spoon to transfer the chicken thighs to a plate. Remove and discard the lemongrass pieces and the tea balls/spice infusers with the star anise and peppercorns. Stir the juice of half a large lime and 1 teaspoon sriracha (or to taste) into the broth.
Shred the chicken with two forks, return the shredded chicken to the pot, then add the cooked rice noodles and stir to combine. Heat 1–2 minutes if needed to warm the noodles through.
Divide the pho among 4 bowls and garnish with finely sliced mint, finely sliced Thai basil, and cilantro. Serve immediately.