To prepare salsa, combine the first 6 ingredients.
To prepare shrimp, combine paprika and the next 7 ingredients (through allspice) in a large zip-top plastic bag. Add shrimp to bag; seal and shake well to coat. Remove shrimp from bag.
Heat 2 1/2 teaspoons oil in a large nonstick skillet over medium-high heat. Add half of shrimp mixture; cook 2 minutes on each side or until done. Remove from pan. Repeat procedure with remaining 2 1/2 teaspoons oil and remaining shrimp mixture. Serve warm with salsa.