Stir together cornmeal, flour, sugar, salt, and baking soda in a medium bowl. Add buttermilk, eggs, and 4 tablespoons oil; whisk until smooth.
Heat a large skillet over medium heat until hot. Add remaining tablespoon oil; swirl to coat, and heat until a drop of batter sizzles upon contact. Working in batches, pour 1/3 cup batter per cake into skillet. Cook, turning once, until golden and cooked through, about 4 minutes.
Repeat with remaining batter (add more oil if needed, and reduce heat if sides brown too quickly). Serve immediately, topped with butter and honey.