Combine flour, salt, and pepper in a large, shallow dish; set aside. Heat a large skillet over medium-high heat until very hot. Dredge chicken in seasoned flour, tapping off excess; set aside. Add 3 tablespoons oil to skillet. When oil is shimmering, add chicken, and cook until lightly browned, about 3 minutes. Turn over, and cook 3 minutes more. Remove chicken to a plate; set aside and keep warm. Wipe skillet clean, if necessary.

Heat remaining 2 tablespoons oil in same skillet. Add mushrooms and cook, stirring occasionally, until mushrooms are dark golden brown and all the released liquid has evaporated, 5 to 7 minutes.

Remove skillet from heat, and add wine. Return skillet to heat, scraping up any brown bits with a wooden spoon. Add garlic, lemon juice, butter, and parsley. Cook for 10 minutes until reduced and slightly thickened. Taste and adjust for seasoning. Pour sauce over chicken and sprinkle with parsley. Serve immediately.