Heat half of the water to boiling and set aside.
In a blender, add the rice and almonds and blend until a fine powder. This may need to be done in batches, depending on the strength of the blender. Add the powder to a large, heat-proof container, then pour the hot water over top. Stir to combine, then add the cinnamon sticks and stir once more.
Allow the mixture to cool to room temperature, then seal and let sit on the counter for 8-10 hours.
Discard cinnamon sticks. Place contents back into the blender, in batches, and blend until smooth. Strain the mixture through a triple layer of cheesecloth and discard the pulp. Throw the liquid back into a blender with the remaining 5 cups of water, again working in batches, and blend until smooth. Slowly stir in the simple syrup until desired sweetness is reached. Keep refrigerated.