In a stand-up mixer with a dough attachment, combine yeast, salt, sugar, water, and 1 tbsp oil. Swirl the mixture with your finger until combined. Let the mixture sit for about fifteen minutes until foamy.
Set the mixture on a low speed and slowly add four cups of flour cup by cup. Wait until one cup is combined before adding another cup.
Once the mixture has come together as a sticky dough and begins to pull away from the sides of the bowl, stop the mixer and dump the dough onto a clean, floured surface.
Knead the dough until elastic and slightly sticky, adding the last cup of flour. Wash the mixer bowl and wipe the inside down with the rest of the olive oil. Cover the bowl tightly with saran wrap and a dish towel. Let rise for two hours in a warm, draftless area.
Once the dough has doubled in size, dump it out on a clean, floured surface and divide into three equal parts. Knead each part for a few minutes and form into balls.
At this point, you can either wrap the dough tightly in saran wrap and put it in a plastic bag to store in the freezer for up to a month or you can use it right away.
If you will be using the dough right away, cover the pieces with a dish towel. Let rest for 15 minutes. In the meantime, put your pizza stone in the oven and preheat it to 500 degrees
Once the pieces have risen slightly, remove one piece from the dish towel and knead it out to form a crust. Keep the other pieces covered as you knead the dough. Work from the inside, out, kneading the crust as little as possible to keep it airy.
Add sauce and toppings and bake at 500 degrees for 10 minutes. Let cool slightly before slicing.