Preheat the oven to 350ºF and prepare a 9x13-inch dish by spraying with nonstick cooking spray.
Combine the flour, baking powder, and salt in a bowl and set aside.
In a large bowl add the 5 egg yolks, 1 ¾ cups of sugar, milk, melted butter, and vanilla. Using an electric hand mixer and mix until the sugar is dissolved. Set aside.
In another medium-sized bowl, use the electric hand mixer to beat the 5 egg whites on high slowly adding in the rest of the sugar. Beat the egg whites until stiff peaks form- around 5-10 minutes.
Slowly fold the egg white mixture into the egg yolk mixture. Hand folding is key to not deflating the egg whites.
Next whisk in the dry mixture until just combined.
Pour the cake batter into the 9x13-inch pan and bake at 350ºF for 40-45 minutes.
When the cake is cooked, remove it from the oven and let it cool for 15-20 minutes.