Into a blender, add 6 cups of cold water, 5 lime wedges, and 1/2 cup of granulated sugar. Blend on high until smooth, ensuring that the lime wedges are well-blended.
Place a fine mesh strainer over a bowl and pour the blender contents into the strainer, making sure to collect the liquid in the bowl below.
Discard the lime pulp and pieces remaining in the strainer. This step ensures a smooth drink without any chunky texture.
Rinse out the blender to avoid any pulp residue. Pour the strained lime juice mixture (from the bowl) back into the blender. Add 1/4 cup of sweetened condensed milk.
Blend again on high until the mixture is smooth and frothy, creating a luscious texture.
Fill a glass with ice and pour the Brazilian lemonade over top. Garnish with slices of fresh lime for a beautiful presentation.