In a large, heavy self-sealing plastic bag, combine the garlic, ginger, five-spice powder, salt, and pepper. Add the duck breasts, seal, and refrigerate for at least 1 hour or up to 24 hours. Remove from the refrigerator 1 hour before cooking.
Preheat the oven to 400°F/200°C/gas 6. In a large ovenproof sauté pan, heat the olive oil over medium-high heat until shimmering. Sear the duck breast, skin side down, for 5 minutes; turn and sear for 5 minutes on the other side. Transfer the pan to the oven and roast for 5 minutes for medium-rare. Transfer the duck breasts to a plate and keep warm.
To make a balsamic jus, pour off the fat from the pan. Return the pan to medium-high heat, add the wine, and stir to scrape up the browned bits from the bottom of the pan. Cook to reduce the wine by half. Add the balsamic vinegar and cook to reduce for several more minutes.
Cut the duck breasts into diagonal slices and serve drizzled with the balsamic jus.