Juice 3 of the limes; set the juice aside. Cut the remaining 2 limes in half along their equators. Segment them as you would a grapefruit, remove any seeds, and set the segments aside.
Put 3 tablespoons of the butter in a small saucepan over medium heat. Stir, scraping down the sides with a rubber spatula, until the butter foam subsides and the butter turns nut