Into a large bowl, sift together the flour, baking powder, baking soda, sugar and salt. Sift together 4 times.
Blend in the shortening until the mixture resembles coarse meal. Add the buttermilk and cranberries, and stir the mixture gently until it forms a sticky dough.
With floured hands, transfer the dough to a well-floured surface and knead it lightly 8 times. Pat out dough 1/2-inch thick; cut out biscuits with a floured 2-inch round cutter.
Arrange the biscuits upside down on a greased baking sheet. (The biscuit cutter pinches the edges together when they are being cut out, so turning the biscuits over after cutting allows them to rise higher.) The biscuits should touch each other.
Bake the biscuits in the middle of the oven for 10-12 minutes, or until they are golden brown. Serve warm.