This paper addresses the challenging problem of determining feed direction and tool orientation at a given cutter contact (CC) point in five-axis free-form surface machining with flat-end mills. The objective is to efficiently determine a feed direction and tool orientation that will avoid both local and global tool gouging and yield a near maximum machining strip width at the CC point. Concurrent determination of the optimal feed direction and tool orientation is a very computationally intensive task and searching for the correct solution would involve exhaustive evaluations of the machining strip width at many feed directions and tool orientations. In this paper, the optimal feed directions and analytical solutions for the optimal tool orientations in five-axis flat-end milling of spherical, cylindrical, and toroidal surfaces are identified first. A toroidal surface inscription method is devised to approximate the local surface geometry at a CC point on a free-form surface by an inscribed toroidal surface. Analytical solutions for toroidal surface machining are then employed to position the flat-end mill at the CC point with the tool feeding in the best toroidal surface inscribing direction. Case studies have demonstrated that the proposed method can efficiently determine a feed direction and tool orientation, corresponding to a near maximum machining strip width.