Preheat the oven to 450 degrees and place the rack in the middle position.
Combine the flour, sugar, baking powder, salt and baking soda in a large bowl and whisk together. (Ingredients 1-5 may be placed in a food processer and pulsed 4-5 times to mix.).
Add pieces of butter and shortening and, using a pastry blender or fork, cut into the dry ingredients until the pieces are about the size of small peas and evenly distributed. If using a food processor, pulse about 15 times, until the mixture resembles coarse meal.
Stir in the buttermilk, mixing with a spatula until the dough comes together in a rough ball. Turn the dough out onto a lightly floured surface and knead gently and briefly, no longer than 30 seconds, until the dough appears uniform. With a rolling pin, roll out the dough to about 1 inch thick. I allow the form to sit for about 5 minutes to allow the glutens to interact so cutting is easier.
Dip a 2 – 2 1/2-inch biscuit cutter in flour, then press straight down through the dough, without twisting (which makes the biscuit tough). Place the dough round upside-down on an ungreased baking sheet. Gather the scraps into another inch-thick piece and cut more rounds until all the dough is used.
Bake for 5 minutes, then reduce the heat to 400 degrees and bake for another 10 minutes, until golden brown. Serve immediately. Note: My picture is of one baked from frozen in a toaster oven.
Note: I prepare the dough then place the individual biscuits on a baking sheet covered with a sheet of wax paper then freeze. Afterwhich, I wrap the individual frozen biscuits in wax paper and place in a ziplock bag, squeezing out the excess air for later use. These may be baked frozen; increase baking time.