In a large bowl, add milk, honey, shortening, and butter together, and microwave about 2 minutes until butter and shortening are mostly melted.
Whisk everything together, and set aside to let cool.
Check temperature of mixture, and when it reaches 110 degrees, whisk in 1 egg. Set aside.
In a the bowl of a stand mixer, combine: 5 cups of flour, yeast, and salt.
Fit the stand mixer with a dough hook, and add the milk mixture to the flour mixture, mixing on low speed until dough is coming together. About 2 minutes.
Then increase the speed of the mixture to medium-low, and knead for about 8-10 minutes, until the dough is smooth and elastic. While kneading, about half way through, if the dough is not coming away clean from the sides, add the remaining ½ cup flour, 2 Tablespoons at a time, until the dough is the coming away from the sides clean.
Turn dough out onto a lightly floured counter, and knead by hand until you get a smooth, round, ball.
Place dough in a large bowl sprayed with non-stick spray. And cover tightly with a piece of plastic wrap sprayed with non-stick spray.
Let rise in place for 1- 1 ½ hours until doubled in size.
Spray a 13 x 9 baking dish with non-stick cooking spray.
Turn dough out onto a clean counter, and stretch into a 15-inch long log.
Cut it into 15 equal sized pieces. And cover with the lightly greased plastic wrap while you work with one piece of dough at a time to form into dinner rolls.