In a food processor, working in batches, pulse salmon just until finely chopped. Scrape into a bowl.
Add cornmeal, shallots, mayonnaise, soy sauce, mustard, garlic, ginger, and five spice to salmon. Gently shape mixture into 10 equal patties about 3 inches wide and 3/4 inch thick; set slightly apart on a sheet of waxed paper or foil.
Pour 1 tablespoon oil into a 10- to 12-inch nonstick frying pan over medium-high heat; when hot, add half the cakes and cook, turning once, until browned on both sides and opaque but still moist-looking in the center (cut to test), 6 to 8 minutes total. As cakes are cooked, transfer to an ovenproof platter and keep warm in a 200° oven. Add remaining tablespoon oil to pan and cook remaining cakes.
Serve with Cilantro-Ginger Aioli.