1. Line two baking sheets with parchment paper and preheat the oven to 425.
2. Combine the butter, sugar, salt and water in a small saucepan over medium heat. Bring to a boil, then remove from the heat and sift the flour into the saucepan, stirring until combined.
3. Return the pan to the heat and stir until the batter dries and pulls away from the side of the saucepan. (It will look like mashed potatoes.)
4. Transfer to a bowl and let cool for 1 minute.
5. Add 1 egg to the bowl and stir until the mixture goes from wet and shiny to dry and resembling mashed potatoes again. Add the next egg and repeat until you have incorporated 4 eggs.
6. In a small bowl, whisk the remaining egg with a pinch of salt.
7. Spoon the batter into a pastry bag fitted with a large tip. Pipe the batter in a circle, about 1 inch high and 1 inch wide. Each one should be about 1 inch apart.
8. Dip your fingers into water and round off any of the choux that has a tip from the piping. Brush the choux with the egg wash.
9. Bake the choux for about 10 minutes or until they have puffed up and are lightly golden brown. Lower the temperature to 350 and continue to bake for an additional 20 minutes. The choux will be dry. Transfer to a baking rack and let cool.
10. Remove the pastry cream from the fridge and spoon into a pastry bag fitted with a small tip. Once the choux have cooled, poke small holes into the bottom of them (I used a straw). Fill the inside of the choux with the pastry cream.