Preheat the oven to 350°F (175°C).
In a bowl, mix the graham cracker crumbs, 1/4 cup sugar, and melted butter until well combined.
Press the crumb mixture into the bottom of a 9-inch springform pan to form the crust.
Bake the crust for 10 minutes, then remove from the oven and let it cool.
In a large mixing bowl, beat the cream cheese, 1/2 cup sugar, lemon juice, lemon zest, and lime juice until smooth.
Fold in the chopped cherries and pistachios.
Pour the cream cheese mixture over the cooled crust in the springform pan.
Bake the cheesecake for 30 minutes or until the center is almost set.
Remove the cheesecake from the oven and let it cool completely.
Refrigerate the cheesecake for at least 4 hours or overnight before serving.
Slice and enjoy the luscious lemon-lime cherry pistachio cheesecake!