Begin by adding the water, yeast, sugar, and 1 cup of flour into a large mixing bowl. Whisk all the ingredients together.
Next, add 4 cups more of flour, salt, and olive oil into the bowl and use a wooden spoon to mix everything together. If the dough is still too sticky to mold, add the remaining ½ cup of flour.
Lightly flour a clean surface and transfer the dough onto it. Knead the dough with your hands until it’s smooth and elastic. Form it into a ball.
Drizzle a generous amount of olive oil into a large bowl to grease it. Then, transfer the dough into the bowl and cover it with a tea towel.
First proof of the pizza dough: proof of the pizza dough by keeping it in a warm, dark place for 1 hour to let it rise.*
Meanwhile, grease two standard baking sheets with olive oil and set aside for later.
After an hour the dough should be almost doubled in size. Punch the dough down and turn the dough onto a floured surface.
Divide the dough in half and then use a rolling pin to roll out each half to fit a standard baking sheet. If you only want to make 1 pizza, see the notes below on how to freeze dough for later.
Second proof of the pizza dough: Transfer the rolled dough onto the greased baking sheets and cover with tea towels. Let the dough rise a second time in a warm, dark place for another 30 minutes to 1 hour.
After the dough has risen a second time, it’s time to decide how you like your pizza crust -- thick or thin. If you like a thicker crust, do not punch the dough down a second time. If you like a thinner crust, punch the dough down again with your hands.
Assemble your pizzas: use a spoon to spread the pizza sauce onto your dough, leaving about a 1-inch crust. Sprinkle the mozzarella and parmesan cheese on top of the sauce and then add your toppings (onion, bell pepper, and Italian seasoning -- or whatever toppings you like!).
Bake the pizza at 450ºF for 10 minutes. Turn the heat down to 375ºF and bake for an additional 15-20 minutes or until the bottom of the pizza crust is golden brown.
Let cool for 5 minutes and then slice. Top with red pepper flakes and more parmesan cheese.