Preheat oven to 350 degrees F and lightly grease a 9 by 5-inch loaf pan.

In a large bowl, combine flour, baking soda, and salt; set aside.

Mash 2 bananas with a fork in a small bowl. Use electric mixer fitted with wire whisk to whip remaining bananas and sugar together for 3 minutes or until banana cream is light and fluffy. Add butter, eggs, and vanilla; beat well and scrape down sides of bowl. Mix in dry ingredients just until incorporated; do not overly blend. Fold in mashed bananas with a rubber spatula. Pour the batter into the prepared loaf pan. Rap pan on counter to get rid of air bubbles.

Bake for 1 hour and 15 minutes, or until golden brown and a toothpick inserted into the center of the loaf comes out clean. Rotate pan periodically to ensure even browning.

Cool bread in pan for 10 minutes or so, and then turn out onto a wire rack to cool completely before slicing.