Preheat oven to 425°F. Line 2 baking sheets with parchment or silicone mats. Set aside.
Dough: In a medium-size saucepan bring water, butter, sugar and salt to a rolling boil.
Remove from heat, mix in flour. Return to burner on medium and stir vigorously with a wooden spoon until the flour begins to pull away from the sides and forms a film on the bottom of the saucepan. The pate a choux should form a ball.
Scrape into a mixing bowl. Using an electric mixer, beat the dough for 1 minute on medium speed to cool slightly before adding 4 eggs one at a time. Stop after each egg to scrape the sides of the bowl. The dough may separate after adding each egg but, will come together when beaten.
Mix until the dough is smooth and glossy and the eggs are completely incorporated.
Use a piping bag fitted with a plain tip to pipe rounds 2 inches in diameter on baking sheets. Leave 2 inches between each puff. Alternately, use a Tbsp using 2 Tbsp dough for each round. Rounds should be approximately 2-inch circles about 1/2 inch high. Leave 2 inches between to allow for spreading.
Beat remaining egg with water. Gently smooth tips of pastry with finger dipped in egg wash then brush each puff with remaining egg wash.
Bake for 15 minutes then lower the oven temperature to 375°F. Bake for an additional 10-15 minutes or until golden and they sound hollow when gently tapped.
Pierce each puff on the side, using the tip of a knife or a skewer to allow steam to release. You won't need a large slit, just a small inconspicuous hole. Cool completely on the baking sheet.
Pastry Cream Filling: Whisk together sugar, cornstarch, and salt in a medium-size heavy bottomed saucepan. Whisk together milk and egg yolks in a glass measuring cup; add to saucepan along with butter and bring to a boil over medium heat. Let boil 1 minute, still whisking; then remove from heat and stir in vanilla.
Strain pastry cream through a fine-mesh sieve into a bowl. Cover with plastic wrap, pressing it directly onto surface of cream to prevent skin from forming. Refrigerate until chilled, at least 2 hours and up to 2 days. Just before using, whisk until smooth.
Fill: use a sharp knife to cut puffs through the middle leaving one side intact. Fill puffs with pastry cream using an open star tip or Tbsp.
Dust with powdered sugar. Serve chilled.