In a small bowl, whisk together olive oil, 3 cloves of minced garlic, oregano, basil, salt, and pepper.
Coat chicken breasts thoroughly with the marinade and let sit for 15 minutes.
Bring a large pot of salted water to a boil and cook spaghetti according to package instructions until al dente.
Heat a grill pan or outdoor grill over medium-high heat and cook chicken for 6-8 minutes per side or until the internal temperature reaches 165 degrees Fahrenheit.
In a large skillet over medium heat, melt the butter and saute the remaining 2 cloves of garlic for 1 minute.
Whisk in heavy cream and simmer for 5 minutes until slightly thickened.
Gradually stir in Parmesan cheese until the sauce is smooth and creamy.
Toss the cooked spaghetti into the Alfredo sauce until evenly coated.
Slice the grilled chicken into strips and serve on top of the pasta, garnished with fresh parsley.