Preheat the oven to 200°C (390°F). In a medium saucepan, add the water, butter, sugar and salt, and bring to a boil over medium-low heat, melting the butter and dissolving the sugar.
Add flour. Remove the pan from the heat and add the flour immediately. With a wooden spoon, beat vigorously until completely combined, and then return to the heat for 2 minutes and continue to beat until the mixture comes away from the sides of the pan and forms a ball. You’ll see a film form on the base of your saucepan, and you’ll know it’s ready.
Beat to release steam. Remove the mixture from the heat and place it in the bowl of a stand mixer fitted with the paddle attachment. Beat for 1 minute on low speed to release some steam. Stop when you don't see anymore steam coming out of the bowl and the mixture has cooled slightly. In a small bowl, whisk 4 eggs together.
Beat in eggs. Increase the speed to medium and add ¾ of the whisked eggs a little at a time, beating well after each addition. Scrape the sides and bottom of the bowl halfway through. It may look curdled to start with but will come together as you beat the mixture. Once the eggs have been fully incorporated, beat the mixture for a further 2 minutes.Note. The perfect consistency. The choux pastry should be smooth and shiny and should hold its shape when piped. Another sign that the batter is ready is when the beater or a rubber spatula is pulled up and a thick V-shaped ribbon forms, of smooth dropping consistency. If your pastry has not achieved this consistency, add the remaining egg and test the consistency again. If you need more egg, then whisk the 5th egg in a small bowl, and add a tiny bit at a time. Stop adding the egg as soon as you get the right consistency. I doubt that you'll need all this egg. Set aside any remaining egg for egg wash.
Pipe choux onto the baking tray. Spoon the choux pastry dough into a piping bag fitted with a 1.3cm (½ inch) plain round nozzle. (You can also use a zip lock bag with the corner cut off for piping.) Line a large baking tray with parchment paper. Whilst holding the piping bag upright and keeping the tip of the piping tip touching the choux pastry, pipe 12 5cm (2-inch) wide mounds onto the prepared tray. Keep them 2.5cm (1-inch) apart. Using a pastry brush dipped in water, brush the parchment paper around the mounds. The water creates steam in the oven, which helps puff up the choux.
Prep choux on the tray. Using the tip of your finger dipped in water, smooth the points of each mound. This stops the peaks from burning in the oven. Add milk into the remaining egg and whisk together. Brush this egg wash gently over the top of the choux pastry mounds.
Bake. Place the tray in the oven and bake for 10 minutes before lowering the oven temperature to 180°C (350°F) and continue to bake for 25 to 30 minutes, or until golden brown and crisp. Skewer a hole in the bottom of each choux bun to allow the steam to escape. Return to the oven for 5 to 10 minutes, and then remove from the oven and transfer to a wire rack to cool completely.