Step 1: In a medium saucepan, combine 1 cup of granulated sugar with 1 cup of water. Heat over medium heat, stirring constantly until the sugar is completely dissolved. Do not bring to a rapid boil. This creates your simple syrup.
Step 2: Remove the simple syrup from the heat and let it cool completely to room temperature. You can place the saucepan in an ice bath to speed up this process.
Step 3: While the syrup cools, prepare the lemons. Roll the lemons firmly on a countertop to help release their juice. Cut them in half and using a citrus reamer or juicer, extract about 1.5 cups of fresh lemon juice. Strain the juice through a fine-mesh sieve to remove any pulp and seeds.
Step 4: In a large pitcher (at least 2-quart capacity), combine the cooled simple syrup and the strained fresh lemon juice. Stir well.
Step 5: Add the remaining 4 cups of cold water to the pitcher. Stir again until all ingredients are thoroughly combined.
Step 6: Taste the lemonade and adjust the sweetness or tartness to your preference. If it's too tart, add a little more simple syrup (if you have extra, or make a small batch). If too sweet, add a splash more lemon juice or cold water.
Step 7: Chill the lemonade in the refrigerator for at least 1 hour before serving. This allows the flavors to meld and ensures it's perfectly cold and refreshing. Serve over ice with lemon slices or fresh mint as garnish.