In a small bowl or measuring cup, mix together the warm water, sugar and yeast. Let sit in a warm place for 15 minutes or until foamy at the top (I like to keep mine in the microwave).
In the bowl of a stand mixer fitted with a dough hook, combine the 5 cups of flour, salt, ½ cup olive oil and water/yeast mixture, and mix on low speed until it has come together. Then continue to mix on medium for 5 minutes until smooth. If it appears extra sticky, add the additional flour (but don't over mix because it will become sticky again)
Remove the dough from the bowl (I found a flexible bench scraper helpful) and place on a floured work surface. Knead two or three times, adding additional flour if needed to prevent the dough from sticking to the surface. Liberally coat the mixing bowl in olive oil and place the dough back into the bowl. Cover the bowl with plastic wrap or a towel and keep in a warm place for about an hour, or until it has doubled in size (again, I use the microwave)
Coat a rimmed baking sheet with the remaining olive oil. When the dough has doubled in size, place it in the pan and begin to press it out evenly with your fingers. Let the dough rise for an additional hour or until it has doubled in size (this is called the proofing stage).
Meanwhile, preheat the oven to 425 F. When the dough has finished proofing, brush the top of the dough with the infused oil. Sprinkle with the course salt and rosemary, followed by a layer of sliced onions and tomatoes. Bake for 25 to 30 minutes. (The tomatoes will release juice as the dough bakes, so don't confuse the moisture for raw dough. That's what makes this recipe so delicious. It will be fully baked and dry on the inside)
Recipe by A Sue Chef at http://www.asuechef.com/tomato-focaccia-with-infused-olive-oil/