1. Rinse shrimp and pat dry; transfer to a bowl. Add 1 tablespoon each oil, lime juice and garlic; toss to combine. Season with salt and pepper. Marinate at room temperature 15 minutes.
2. Meanwhile, whisk together remaining 2 tablespoons lime juice, 14 teaspoon garlic, the orange juice and jalapeno. Add 4 tablespoons oil in a slow stream, whisking until combined well. Stir in onion and cilantro; salt and pepper to taste, for vinaigrette.
3. Heat remaining 1 tablespoon oil in a large nonstick skillet. Add shrimp, in 2 batches, and cook, turning once, until golden brown and opaque, about 3 minutes per batch. Transfer, as cooked, to a plate.
4. Combine greens, mango, papaya and almonds in a large bowl.
5. Toss with enough vinaigrette to coat; salt and pepper to taste. Mound salad on plates alongside shrimp and serve.