Preheat oven to 375 degrees F. Lightly grease 2 baking sheets or line with parchment paper.
In a heavy saucepan bring water to a boil with butter and salt over high heat and reduce heat to moderate. Add flour all at once and beat with a wooden spoon until mixture pulls away from side of pan.
Transfer mixture to a bowl and with an electric mixer on high-speed beat in 4 eggs, 1 at a time, beating well after each addition. Batter should be stiff enough to just hold soft peaks and fall softly from a spoon. If batter is too stiff, in a small bowl beat remaining egg lightly and add to batter a little at a time, beating on high speed, until batter is desired consistency.
Stir Gruyere into pate a choux and arrange level tablespoons about 1-inch apart on baking sheets. Bake in upper and lower thirds of oven, switching position of sheets halfway through baking, 30 minutes, or until puffed, golden, and crisp.
Gougeres keep, chilled in sealable plastic bags 2 days or frozen 1 week. Reheat gougeres, uncovered in a preheated 350 degree oven 10 minutes if chilled or 15 minutes if unthawed frozen.