Position a rack in the middle of the oven, remove any racks above, and preheat to 350°F. Coat a 12-cup bundt or tube pan with baking spray and set aside.
Finely grate the zest of 3 of the oranges, then squeeze 4 of them. You should have 1½ cups of juice; if not, squeeze the 5th orange, then set aside.
In a large bowl, whisk together the flour, baking powder, and salt.
In the bowl of a stand mixer fitted with a paddle attachment, or with a handheld mixer in a large bowl, beat the eggs on medium-high speed until well-combined, about 1 minute. Slowly pour in the granulated sugar and continue beating until thick and pale yellow, about 3 minutes. On low speed, alternate adding the flour mixture and oil, starting and ending with the flour, and beat until just a few wisps of flour remain. Pour in the orange juice and zest and whirl for a few seconds to bring the batter together.
Pour the batter into the prepared pan and bake until a cake tester comes out with a few moist crumbs clinging to it, about 1¼ hours. If the top is browning too much as the cake bakes, cover lightly with foil. Transfer to a wire rack and cool for 15 minutes.
Turn the cake out onto the rack and cool completely, then place it in a covered cake stand and let it sit overnight. Just before serving, dust the cake with powdered sugar.
Notes
Make sure to use a lightly-colored bundt pan. A dark one will turn out a cake that sticks and is unpleasantly brown.
Since this cake only gets better with age, don't even think about taking a bite until the day after you make it, or even the day after that.