We describe a new approach to ray tracing which drastically reduces the number of ray-object and ray-bounds intersection calculations by means of 5-dimensional space subdivision. Collections of rays originating from a common 3D rectangular volume and directed through a 2D solid angle are represented as hypercubes in 5-space. A 5D volume bounding the space of rays is dynamically subdivided into hypercubes, each linked to a set of objects which are candidates for intersection. Rays are classified into unique hypercubes and checked for intersection with the associated candidate object set. We compare several techniques for object extent testing, including boxes, spheres, plane-sets, and convex polyhedra. In addition, we examine optimizations made possible by the directional nature of the algorithm, such as sorting, caching and backface culling. Results indicate that this algorithm significantly outperforms previous ray tracing techniques, especially for comples environments.