Preheat the oven to 350F/180C.
Grease 3 8" cake pans and line them with parchment paper. (Russian sponge is very delicate so it's important to use parchment paper for easy removal.)
Crack 5 eggs at room temperature to a bowl of a stand mixer and add sugar and vanilla, beat at high speed for 5 minutes until the mixture is pale and triples in volume.
Fold in flour through a sifter in 5-6 additions blending it in gently after each addition. Your goal is to keep the volume of the egg mixture so be very careful in this step of the process.
Divide your cake batter among 3 pans and bake for 25-30 minutes until cake tester or tooth pick comes out clean and the cakes have risen to the top of the pan. (I baked 2 layers and then 1 later).
Cool for 10 minutes and then run a knife around the edges of your pans to release the cakes and flip them over on a wire rack to cool completely.
(After your cakes have cooled you can individually wrap them in plastic wrap for later use. You can bake you sponge layers a day ahead.)