Heat oven to 350 degrees.
Grease and flour two 8-inch round layer cake pans.
Grate the rind from 2 of the oranges.
Peel 3 of the oranges, removing all the white next to the pulp.
Discard the peelings.
Section these oranges, discarding membrane and seeds.
Cut the sections into very tiny pieces.
Squeeze the remaining orange and add the juice to the cut-up oranges.
Measure out 1 1/4 cups of this mixture.
Add 1/2 cup sugar and stir well until sugar is dissolved.
Take out 1/4 cup of mixture and set aside for icing.
Cream shortening well.
Add 1 cup sugar gradually and cream well after each addition.
Sift flour, baking powder, soda and salt together and add to creamed mixture alternately with the orange-sugar mixture.
Stir in 1 tbsp. grated orange rind.
Beat egg whites until stiff but not dry.
Fold in.
Pour into prepared pans and bake about 25 minutes or until tops spring back when touched lightly in the centre.
Turn out on racks and cool.
Fill and ice with orange cream icing.
Sprinkle top with remaining grated orange rind.