The purpose of this paper is to locate five points Pi ( l ≤ i ≤ 5 ) in a closed unit cube C such that is as large as possible, where d(Pi, Pj) denotes the distance i j between Pi and Pj. We prove that this minimum distance cannot exceed (=m, say), and if it is equal to m, then the corresponding configuration is congruent to the set of points shown in fig. 1, namely P1 = A1 (0,0,0), P2 = A8 (1, 1, 1), P3 = B1 (0,1/2,1), P4 = B3 (1/2,1,0) and P5 = B5 (1, 0, 1/2).