Oregon is never going to win the majority of its battles for 5-star prospects over USC/UCLA. Never. So get over it.
Why? Primarily, it's an issue of location. The vast majority of 5-star prospects on the West Coast play high school football near USC/UCLA. Further, the Trojans have the huge advantage of being perhaps the preeminent college football program in the nation, winning 11 national titles while producing the most NFL first-round draft picks and NFL Hall of Famers.
Oregon lost the 2010 national title game to Auburn on a last-second field goal. It whipped unbeaten defending national champion Florida State by 39 points in the first College Football Playoff semifinal. It beat Wisconsin in the 2012 Rose Bowl and Kansas State in the 2013 Fiesta Bowl. Oregon has won at least 10 games and finished ranked in the top-11 for seven consecutive years. It has finished ranked in the top five in four of the past five years.
Oregon just needs to keep doing what it's been doing for the past six or seven years, which is trying to ... well ... win the freaking day. That probably includes a steady, but incremental, improvement in the quality of recruits. But becoming obsessed with 5-star recruits is the worst thing the Ducks could do. It is the path to failure.