Bring a large pot of salted water to a boil. Fill a large bowl with ice water. Cook the beans in the boiling water until bright green and al dente, about 5 minutes. Drain and immediately plunge the beans into the ice water. Drain again and pat dry.
Meanwhile, using a sharp knife, peel 4 of the oranges, removing all of the bitter white pith. Working over a bowl, cut in between the membranes to release the sections into the bowl. Zest one of the remaining oranges and juice both of them. Transfer the juice to a saucepan and add the vinegar and honey. Bring to a boil, then simmer over moderate heat until reduced to a syrup, 10 minutes. Season with salt.
Transfer the beans and orange sections to a platter and drizzle the syrup on top. Garnish with the orange zest and serve.