In a large mixing bowl, combine water, yeast, sugar, and 1 cup of flour. Whisk until blended.
Add 4 more cups of flour, salt, and olive oil. Mix with a wooden spoon. If dough is sticky, add remaining ½ cup of flour.
Transfer dough to a floured surface. Knead until smooth and elastic, then shape into a ball.
Grease a large bowl with olive oil. Place dough inside, cover with a towel, and let rise in a warm, dark place for 1 hour.
Preheat oven to 400ºF. Grease two baking sheets with olive oil.
After proofing, punch dough down and divide in half. Roll out each half to fit a baking sheet.
Transfer rolled dough to baking sheets. Cover and let rise again for 30 minutes to 1 hour.
Decide on crust thickness. For thicker crust, skip second punch-down.
Spread sauce on dough, leaving a 1-inch crust. Add cheeses, toppings, and seasoning.
Bake at 450ºF for 10 minutes. Reduce heat to 375ºF and bake for 15-20 minutes until golden.
Cool for 5 minutes, then slice. Sprinkle with red pepper flakes and extra parmesan.