Preheat Oven: Preheat your oven to 350°F (175°C). Grease a 9×13-inch baking pan with baking spray or butter and flour.
Prepare Dry Ingredients: In a medium bowl, sift together the flour, baking powder, and baking soda. Set aside.
Whip Egg Whites: In a large stand mixer, whip the 5 egg whites on medium-high speed until stiff peaks form. (The egg whites should stand up when the whisk is removed.) Transfer the whipped egg whites to a clean large bowl.
Cream Butter and Sugar: In the same stand mixer bowl, add the butter and sugar and beat on medium speed until light and fluffy, about 1-2 minutes.
Add Egg Yolks: Add the egg yolks one at a time to the butter mixture, beating after each addition. Then, add the vanilla extract and whole milk, mixing until combined.
Combine with Dry Ingredients: Gradually add the flour mixture to the wet ingredients and mix until just combined. Then, gently fold the batter into the whipped egg whites until fully incorporated.
Bake the Cake: Pour the batter into the prepared baking pan and bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Make the Milk Mixture: While the cake is baking, whisk together the heavy cream, sweetened condensed milk, and evaporated milk in a large bowl.
Soak the Cake: Remove the cake from the oven and use a fork to pierce it all over. Slowly pour the milk mixture over the warm cake, ensuring it absorbs evenly. Cover the cake and refrigerate for at least 3-4 hours, or overnight.
Top with Whipped Cream: Before serving, spread whipped cream evenly over the cake and sift ground cinnamon on top for garnish.