Fill a shallow dish with warm water. Dip a rice paper wrapper in the water for a few seconds until it becomes soft and pliable. Place the wrapper on a clean, damp towel. On the bottom third of the wrapper, add shrimp and a sprinkle of each of the shredded carrots, lettuce, cilantro, mint leaves, and chopped peanuts. Fold the sides of the wrapper towards the center and then roll it tightly from the bottom up. Repeat with the remaining ingredients.