Cook the pasta: Bring a large pot of salted water to a boil. Cook the linguine until just shy of al dente (about 1 minute less than package directions). Reserve 1 cup of pasta water, then drain.
Season the shrimp: Pat the shrimp very dry with paper towels — this is the key to a good sear. Season with 1/2 teaspoon salt, the black pepper, and red pepper flakes.
Sear the shrimp: Heat 1 tablespoon butter and the olive oil in a large skillet over medium-high heat. Add the shrimp in a single layer and cook 1 1/2 to 2 minutes per side, until pink and just opaque. Transfer to a plate. (Work in two batches if needed to avoid crowding.)
Build the sauce: Reduce the heat to medium. Add the remaining 4 tablespoons butter and the garlic; cook 30 seconds until fragrant but not browned. Pour in the white wine, scraping up any browned bits, and simmer 2 minutes until slightly reduced.
Finish the sauce: Stir in the lemon juice, lemon zest, and 1/2 cup of the reserved pasta water. Simmer 1 minute until the sauce looks silky.
Toss it together: Return the shrimp to the skillet along with the drained linguine, parsley, and parmesan. Toss for 1 minute, adding more pasta water as needed until the sauce glossily coats everything. Season with the remaining 1/2 teaspoon salt to taste.
Serve: Divide among warm bowls, top with extra parmesan, parsley, and a pinch of red pepper flakes. Serve immediately.