Drizzle 3 tablespoons hot sauce on top of chicken. Cook for 4-5 hours on high, or 6-7 hours on low, until chicken is cooked but still moist and fall-apart tender. Just before serving, shred chicken.
Stir together cheese, Greek yogurt, remaining 2 tablespoons hot sauce, and basil. Mix until all ingredients are thoroughly combined and cheese is melted.
The exact heat and speed of cooking can vary between different slow cookers. Some slow cookers, especially newer models, may cook hotter and faster than others.