Place the sugar, corn syrup, water, butter, and salt into a large saucepan. Attach a cooking thermometer to the side of the pan. Heat over medium heat, stirring constantly with a mixing spoon until the mixture begins to boil and the sugar dissolves completely, about 5-7 minutes. Continue cooking without stirring until the syrup reaches 250°F (hard ball stage).
Remove the saucepan from heat and carefully pour the hot syrup over the prepared popcorn in a large mixing bowl. Immediately stir to coat all the popcorn evenly, listening for a gentle bubbling sound and watching the mixture thicken as the syrup cools slightly.
Once the mixture is cool enough to handle but still sticky, use greased or buttered hands to shape the coated popcorn into 10 individual balls. Press gently and compact each ball, ensuring it holds together.
Place each popcorn ball on wax paper or parchment-lined tray. While still warm, sprinkle the tops with colorful sprinkles, pressing lightly to adhere them to the surface. Allow the popcorn balls to cool completely and set for at least 15 minutes.
Serve the popcorn balls at room temperature, displaying their bright colors and crunchy, chewy texture. These festive treats are ready to enjoy!