Process strawberries in a blender or food processor until smooth, stopping to scrape down sides as needed. Press strawberries through a large wire-mesh strainer into a medium bowl, using back of a spoon to squeeze out juice; discard pulp and seeds. Combine sugar and cornstarch in a 3-qt. saucepan; gradually whisk in strawberry puree and fresh lime juice. Whisk in 3 large eggs and 2 egg yolks. Bring mixture to a boil over medium heat, whisking constantly, and cook, whisking constantly, 1 minute. Remove from heat, and whisk in butter. Place plastic wrap directly on warm curd (to prevent a film from forming); chill 8 hours. Serve with hot biscuits, Strawberry-Lemonade Muffins, or use as a filling for tart shells.