Combine the sugar with 1 cup of the water in a small saucepan. Bring the mixture to a boil, then turn off the heat and stir until the sugar is fully dissolved to make a simple syrup. Set aside to cool.
Pour the lime juice into a 2-quart pitcher. Add the cooled simple syrup and stir well.
Stir in the remaining 4 cups of cold water.
Chill for at least 30 minutes, then serve over ice. Garnish with lime slices if you like.
Notes
Storage: Store the limeade in a covered pitcher or airtight container in the fridge. It’ll keep for up to 5 days. Give it a good stir before serving; sometimes the juice settles a bit. Don’t add ice until you’re ready to serve, so it doesn’t get watered down.