Divide dough evenly into 5 pieces; pat each dough piece into a 5-inch circle. Spoon about 1/2 cup spinach mixture onto half of each circle, leaving a 1/2-inch border. Fold dough over filling until edges almost meet. Bring bottom edge over top edge; crimp edges of dough with fingers to form a rim.
Place calzones on a baking sheet coated with cooking spray.