In a large pot, bring salted water to a boil and add 3 pounds of whole, unpeeled potatoes. Cook until fork-tender, about 20-25 minutes. Drain and cool slightly, then peel and chop into cubes.

While the potatoes cool, place 5 large eggs in a saucepan filled with water. Bring to a gentle boil, then cover and remove from heat. Let them sit for about 12 minutes.

Transfer eggs to an ice bath to cool. Once chilled, peel and chop, reserving one for garnish.

In a large mixing bowl, combine 1 cup mayonnaise, 3 tablespoons yellow mustard, 3 tablespoons sweet pickle relish, ½ teaspoon salt, and ½ teaspoon black pepper. Mix until smooth.

Gently fold in chopped potatoes, 4 chopped eggs, ½ cup diced celery, and ¼ cup diced onion. Stir gently to coat without breaking the potatoes.

Transfer salad to an airtight container and refrigerate for at least 2 hours or overnight to meld flavors.

Before serving, gently stir the salad and adjust seasoning. Spoon into a serving dish, garnish with paprika and reserved egg slice.