Heat the oven to 350°F/175°C.

Slice 2 of the oranges crosswise into thin full rounds. Halve the remaining 3 oranges, then slice into thin half-moons. In a wide saucepan, combine the water and sugar and bring to a simmer over low heat. Add the orange slices and cook gently for 10 minutes, until softened and translucent. Using tongs, transfer the slices to a plate. Reserve the syrup.

Line the bottom and sides of a 9.5-inch/24 cm round cake pan with parchment paper. Arrange the orange slices in overlapping concentric circles, using the full rounds first and filling gaps with the half-moons. Set aside.

In a large bowl, rub the orange zest into the sugar with your fingers to release the oils. Add the eggs, oil, and orange juice and whisk until well combined. Add the flour, baking soda, baking powder, and salt, and whisk just until smooth.

Pour the batter gently over the orange slices. Bake for about 50 minutes, until the cake is golden and a skewer inserted in the center comes out with a few moist crumbs.

Let cool in the pan for 5 minutes. Invert onto a serving plate and remove the parchment. Brush the orange layer with the reserved syrup.

Let cool slightly before serving. The upside down orange cake keeps at room temperature for up to 3 days.