jmc

Not considering rotations and reflections, there are 8 ways to choose the first bead to put on the necklace, followed by 7, 6, 5, and 4 ways to choose the next beads. For each arrangements of beads on the necklace, there are 5 ways to rotate it and another 5 ways to reflect it and then rotate it to another arrangement. Thus, arrangements of beads on the necklace come in groups of 10 equivalent arrangements. The total number of different arrangements is therefore $8\cdot 7\cdot 6\cdot 5\cdot 4/10=\boxed{672}$.