Dice 1 cup of the pineapple into very small pieces, set aide.
Bring sugar and 1 cup water to a boil in a saucepan, stirring until sugar dissolves. Take off heat and add lime zest. Let steep for 10 minutes and liquid cools.
Strain lime syrup into blender (discard lime zest) with remaining 4 cups cubed pineapple chunks and puree. Strain through a sieve is optional. Add the 1 cup of diced pineapple to the blended mixture and stir to incorporate. Transfer mixture to a bowl and refrigerate until chilled.
Pour pineapple mixture into eight 3–ounce ice-pop molds. Top with cover and insert wooden sticks or handles that come with your ice-pop mold kit. Transfer molds to the freezer for 3 hours or more.
If you don't have a mold kit with a top lid that positions the wooden popsicle sticks, transfer molds to the freezer and freeze until slightly slushy, about 1 hour. Insert a popsicle stick into each mold and freeze until ice pops are solid, about 3 hours or more.
To release ice pops from molds, run the bottom of the molds briefly under warm water and push up from bottom.