In a medium bowl, soak the chiles and 2 garlic cloves in 2 cups warm water until the chiles are soft, 30 to 45 minutes. Drain, reserving the soaking liquid. In a blender, puree the chiles, garlic and 1 1/3 cups soaking liquid. Season the chile sauce with salt and pepper.
Place the beef shanks in a large, heavy pot. Add the stock and 8 cups cold water, adding more water if needed to cover the shanks completely. Add the onion, carrots, celery, bay leaves and the remaining 3 garlic cloves. Season with 2 tbsp. salt and 1 tbsp. pepper. Bring to a boil, then reduce the heat to medium-low. Cover and simmer, occasionally skimming the fat from the surface, until the meat is tender, about 2 1/2 hours.
Transfer the shanks to a cutting board; let cool 15 minutes. Strain the soup into a large bowl; return the liquid to the pot. In a blender, puree the strained vegetables; stir into the soup. Add the hominy, bring to a boil, reduce heat to low and let simmer.
Meanwhile, using two forks, shred the meat (discard the fat and bones). Return the meat to the pot; season. Let simmer until heated through, about 5 minutes. Ladle the soup into bowls and garnish with the cabbage, radishes and oregano. Drizzle with the chile sauce. Serve with lime wedges and tostadas.