Preheat the oven to 170C/150C Fan/Gas 3. Lightly grease a 23cm/9in springform cake tin with butter.
Zest three of the oranges into a large mixing bowl and set aside.
Remove the pith from the three zested oranges and discard. Roughly chop the orange flesh, removing any seeds as you go, and place it into the bowl of a food processor. Blend well, adding the rapeseed oil as you blend until the mixture is smooth and well combined. Set aside.
Add the eggs and 250g/9oz of the caster sugar to the bowl containing the orange zest. Using an electric whisk, whisk the mixture until it is pale, thick and creamy, and leaves a trail when the whisk is lifted from the mixture.
Stir together the flour, ground almonds and baking powder in a separate bowl.
Carefully fold half of the puréed orange mixture into the egg mixture.
Fold in all of the flour, then fold in the remaining puréed orange mixture.
Pour the cake mixture straight into the prepared cake tin and bake in the oven for 1 hour, or until golden-brown and risen. Check the cake is cooked by inserting a clean skewer or knife into the centre – if it comes out clean, then the cake is ready; if not, cook it for a further 5 minutes and check once more.
While the cake cooks, prepare the frosting. Whisk the cream cheese, crème fraîche and icing sugar together in a bowl until smooth and thick, then chill in the fridge, covered, until needed.
Peel the remaining 2 oranges with a vegetable peeler, then julienne the zest very finely.
Pour 150ml/5fl oz of cold water into a saucepan and stir in 150g/5oz of the remaining caster sugar. Add the julienned orange peel, then bring the mixture to the boil. Reduce the heat until the mixture is simmering and simmer for 8-10 minutes to make a light syrup.
Strain the julienned orange zest through a sieve suspended over a large bowl (the orange-scented sugar syrup can be chilled and used in an orange drizzle cake recipe or another recipe).
Sprinkle the remaining caster sugar onto a plate and dredge the julienned orange zest in it until coated.
Remove the cake from the oven and set aside to cool slightly in the tin, then turn it out set aside to cool completely on a wire rack.
When the cake has cooled, spread the cream cheese frosting over the top and decorate with the chopped walnut pieces, candied orange zest and basil cress, if using.