Preheat oven to 400°. Cut stems from beets, leaving 1/2 inch attached. Clean beets well and toss with 2 tablespoons olive oil, 1/4 teaspoon salt, and 1/8 teaspoon pepper.

Place beets in a roasting pan with 1/4 inch water in bottom. Cover with foil and roast until tender when pierced with a knife, about 1 hour. Transfer beets with a slotted spoon to a plate, and let cool. Trim stems, peel, and cut into 1/4-inch-thick slices.

Into a small bowl, squeeze juice from 1 orange; add lemon juice, remaining 2 tablespoons olive oil, shallots, vinegar, and remaining 1/4 teaspoon salt and 1/8 teaspoon pepper.

With a sharp paring knife, cut tops and bottoms off remaining 4 oranges. With orange sitting on its cut bottom, use knife to remove peel and pith. Slice oranges into pinwheels.

In a bowl, gently toss beets with half of the vinaigrette; arrange on a platter. Spoon oranges around beets; drizzle with remaining vinaigrette. Sprinkle with mint.