Place half of strawberries (2 1/2 cups) into a blender and pulse to create a lumpy puree (don’t make it completely smooth). Pour puree into a medium saucepan over medium heat.
Pour puree into a medium saucepan over medium-high heat.
Stir the sugar into the strawberry puree and continue to stir until the sugar dissolves and the mixture comes to a low boil.
Whisk the cornstarch into the 1/2 cup water to blend. Pour into the strawberry mixture in the saucepan, stir to combine and allow to come to a low boil, stirring constantly.
Lower the heat to medium-low and stirring constantly allow the mixture to thicken and become glossy and transparent; aproximately 4 minutes.
Remove filling from heat. Stir in the lime juice and the remaining 2 1/2 cups of quartered strawberries.
TIP: Before pouring filling into pie crust, place pie crust on a small baking sheet to steady it when chilling in the refridgerator. Pour filling into prepared pie shell.
Allow to cool slightly (10-15 minutes) before chilling for several hours or overnight until firm. NOTE: if the pie is warmer than room temperature, leave uncovered in the refridgerator until cool to prevent condensation from forming and dripping on the pie. Once it is cool it may be covered.
Top with whipped cream and serve.