Dissolve yeast in warm water in a large bowl and let stand for 5 minutes. Stir in 3 cups flour and the salt, stirring until smooth. Stir in an additional 2 cups flour; continue adding flour (up to 1/2 cup), 1 tablespoon at a time, stirring until dough comes away from bowl but is still sticky.
Turn dough out onto a lightly floured work surface, and knead with lightly floured hands. Start by slapping the dough onto the counter, pulling it toward you with one hand and pushing it away from you with the other. Fold the dough back over itself (use a bench scraper or a wide knife to help scrape dough from surface). Repeat until it's easier to handle, about 10 times. Finish kneading normally until dough is smooth, elastic, and soft, but a little tacky, about 10 minutes.
Shape dough into a ball and transfer to a lightly oiled bowl; turn to coat. Cover with plastic, and let rise in a warm place until it doubles in volume, 3 hours. Press it with your finger to see if it's done; an indent should remain.
Place a pizza stone (available at most kitchen supply stores) on floor of gas oven (remove racks) or bottom rack of electric oven. Preheat oven to at least 500 degrees for 1 hour.
Meanwhile, scrape dough out of the bowl onto floured surface, and cut it into 4 pieces. Shape into balls. Dust with flour, and cover with plastic. Let rest, 20 to 30 minutes, allowing dough to relax and almost double.
Holding top edge of 1 dough ball in both hands, let bottom edge touch work surface (refrigerate remaining balls as you work). Carefully move hands around edge to form a circle, as if turning a wheel. Hold dough on back of your hand, letting its weight stretch it into a 12-inch round. Transfer dough to a lightly floured pizza peel (or an inverted baking sheet). Press out edges using your fingers. Jerk peel; if dough sticks, lift, and dust more flour underneath.
Arrange desired toppings on dough.
Heat oven to broil. Align edge of peel with edge of stone. Tilt peel, jerking it gently to move pizza. When edge of pizza touches stone, quickly pull back peel to transfer pizza to stone. (Do not move pizza.) Broil until bubbles begin to form in crust, 3 to 4 minutes. Reduce temperature to 500 degrees, and bake until crust is crisp and golden brown, 6 to 8 minutes more. (If not using broiler, bake pizza for 10 to 15 minutes total.) Remove pizza from oven using peel, and top with additional toppings if using. Slice and serve. Repeat with remaining dough and assorted toppings (each variation can be multiplied, depending on the number of pizzas you're making).