Preheat over to 375 with racks in upper and lower thirds.

Cook bacon in skillet over medium heat, turning occasionally, until crisp. Drain on paper towels, then finely chop.

Pour off fat from pan, then wipe clean. Add corn and pan-roast over medium heat, stirring until kernels are mostly golden brown, 10 to 15 minutes

Bring water to a boil with butter and salt in a heavy medium saucepan, stirring until butter is melted. Add flour all at once and cook over medium heat, stirring vigorously with a wooden spoon, until mixture pulls away from side of pan, about 2 minutes. Remove from heat and cool slightly about 3 minutes.
Add 4 eggs, 1 at a time, beating well after each addition. (Batter will appear to separate at first but will then become smooth.) Mixture should be glossy and just stiff enough to hold soft peaks and fall softly from a spoon. If batter is too stiff, beat remaining egg in a small bowl and add to the batter 1 teaspoon at a time, beating and then testing batter until it reaches proper consistency.Stir in bacon, corn, cheeses, chives, and 1/2 teaspoon pepper.

Line 2 large baking sheets with parchment paper or lightly butter sheets.

Fill a pastry bag fitted with a 1/2-inch plain tip with batter and pipe about 35 (3/4-inch-diameter) mounds, or spoon mounded teaspoons, 1/4 inch apart, onto each sheet.

Bake, switching position of sheets halfway through baking, until puffed, golden, and crisp, 25 to 30 minutes total. Transfer to a rack (still on parchment if using).

Make more puffs on cooled baking sheets. Serve warm or at room temperature.