Put a 10-inch cast-iron skillet in the oven and heat the oven to 425°F.
Whisk the cornmeal, flour, sugar, baking powder, baking soda and salt in a large bowl.
Whisk the buttermilk, eggs and 3 tbsp melted butter in a second bowl.
Fold the wet ingredients into the dry ingredients just until no flour pockets remain.
Carefully add the remaining 2 tbsp butter to the hot skillet and swirl until it foams across the bottom and sides.
Pour in the batter; it should sizzle around the edge immediately.
Bake until the top is golden, the edges pull away and a tester comes out clean, 20 to 22 minutes.
Cool in the skillet for 10 minutes before cutting into wedges.