Preheat the oven to 350 degrees.
Spread 2 c of the coconut on a baking sheet and place in the preheated oven for 5-7 minutes, or until coconut is lightly toasted. Toss the coconut once or twice during cooking to ensure even browning – and be careful not to allow it to burn. Transfer toasted coconut to a shallow bowl or a cool cookie sheet to cool completely.
In a large mixing bowl, combine the remaining 3 c of coconut, the sweetened condensed milk, corn syrup and vanilla. Beat by hand or with an electric mixer until well blended. Slowly add the powdered sugar and continue beating for 2 more minutes. Place the mixture in the refrigerator until cold throughout.
With your hands, form the chilled mixture into 1" balls. Roll each ball in the toasted coconut, making sure that each ball is thoroughly and generously coated. Place the coated balls on a flat platter or cookie sheet in the freezer for at least one hour before serving.
Store the snowballs in an airtight container in the freezer for up to one month.