Whisk lime juice,ginger and mustard in small bowl. Slowly whisk in 4 tbsp oil. Season dressing with salt and pepper.
Brush salmon on both sides with 1 tbsp oil;sprinkle with salt and pepper, then 1 tbsp dill and 1 tbsp basil. Press herbs to adhere. Heat 1 tbsp oil in large nonstick skillet over medium-high heat. Add salmon,herb side down;saute 4 minutes. Turn over;saute until salmon is just opaque in center, about 5 minutes.
Toss greens with remaining herbs and some dressing. Divide between two plates. Top with salmon and remaining dressing.