Fiveleapers a-leaping

The problem of finding knight's tours on a chessboard is well documented in the literature of Recreational Mathematics and is also known in ORMS circles as an instance of the Traveling Salesperson Problem (TSP). A similar but much lesser known puzzle taken from the whimsical world of Fairy Chess is that of identifying fiveleaper tours. A knight move may be described as having coordinates {1,2} meaning in a single move it travels one square in a particular direction and two squares in an orthogonal direction. Using this notation the legal moves for a fiveleaper have coordinates {0,5} or {3,4}. In either event the Euclidean distance traveled is five squares.