In a stand mixer with a dough hook attached, combine yeast and water and let it sit for a few minutes until it gets bubbly.
Add oil, salt and 4 cups of flour. Mix until combined. Add the remaining 1 cup of flour in 1/4 cup increments until the dough pulls away from the sides of the mixing bowl. The dough should be soft and not overly sticky. Let the mixer knead the dough for 5 minutes.
Remove the dough hook, cover the bowl and let it rise for 30 minutes.
Remove dough and separate into 4 even pieces. You are going to stretch the dough out instead of rolling it. This is where you can make your pizza shine!
On a clean work surface, pour a small amount of oil (1-2 tablespoons) and rub it around with your hands so that you also get some on your hands. This will keep the dough from sticking to the counter and give you a golden crust.
Flatten the dough into a disc using the palm of your hand. Next, use your fingers to press the dough out from the center to widen it into a circle. It should be about 6 inches across at this point. If you feel like your dough shrinks back quickly and won't hold its shape, let it rest for 10 minutes covered with a clean kitchen towel and then try flattening it out again.
This step is stretching your dough. Carefully pick up the dough with both hands on one edge and let the rest of the dough hang down. Rotate the dough like you are turning a steering wheel, moving your hands in one direction pulling the dough from hand to hand. You should end up with a circle that is about 11 inches in diameter. If it isn't perfectly round, no worries!
It is ok if there are holes or thin spots - this is where you can fix them. Carefully lay your dough onto a prepared pizza peel, stone or baking pan. If there are holes or thin spots, carefully pinch the dough together in those spots and then gently flatten with your palm. If there are spots that are much thicker than others, press them out with your palm.
If you are using a pizza peel and are going to transfer your pizza to a pizza oven or pizza stone, give the peel a shake to make sure that the dough isn't sticking to the peel and so it will easily slide off.
Now add your toppings! If you are baking in the oven, preheat to 475℉. If you have a pizza stone, place the stone in your oven now to get hot.
Once your toppings are on your pizza, bake for 13-15 minutes or until the crust is golden brown and the cheese is melted and bubbly in the middle of your pizza. If you are using a pizza oven, cook according to your oven's directions.
Remove the pizza from the oven, slice and enjoy!