Heat sesame oil in skillet over medium heat until it bubbles around the tip of a spoon when dipped in.
Mix salmon, eggs, panko, bell pepper, green onions, ginger, soy sauce, sesame seeds, and five-spice powder together in a bowl. Form mixture into patties and set, evenly spaced, into the hot oil in the skillet.
Brown patties, 4 to 5 minutes. Flip and brown on the other side, 4 to 5 minutes more. Remove patties from pan and drain on a paper-towel lined plate to drain excess oil.