Zest and juice 1 orange; reserve. Cut the peel and white pith from the remaining orange. Slice the orange into half-moons and put into a bowl. Add the fennel, 4 teaspoons olive oil, vinegar, and 1 teaspoon salt; toss to coat and set aside.
Toss the shrimp with the remaining 1 tablespoon olive oil; sprinkle with salt. Sear the shrimp in a hot skillet for 45 seconds, then flip. Add 2 tablespoons orange juice, 1 teaspoon orange zest, and butter; cook until the shrimp is opaque in the center, 1 to 2 minutes.
Serve the fennel salad with the shrimp.
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