Put the noodles in a large bowl and cover with boiling water. Let soak until just pliable, about 5 minutes. Transfer the noodles to a colander and drain, shaking and tossing the noodles once or twice.
Meanwhile, in a small bowl, whisk the fish sauce, brown sugar, lime juice, and chiles.
Heat 3 tablespoons oil in a wok or large cast iron pan over high until shimmering. Add the shallots and garlic and cook, stirring frequently, until lightly browned, 1 to 2 minutes.
Add the shrimp and cook, stirring occasionally, until they begin to curl and turn pink, about 2 minutes. Transfer the shrimp to a plate.
Add the remaining 2 tablespoons oil to pan. Add the eggs and cook, stirring occasionally, until nearly set, about 1 minute.
Add the scallions and toss everything together, keeping the eggs relatively intact.
Add the noodles, shrimp, and fish sauce mixture; stir-fry until the noodles are evenly coated, 2 to 3 minutes.
Transfer the pad Thai to a platter. Top with peanuts, cilantro, and bean sprouts and serve with lime wedges.
