We report the discovery of a unique gravitational lens system, SDSSJ2222+2745, producing five spectroscopically confirmed images of a z_s=2.82 quasar lensed by a foreground galaxy cluster at z_l=0.49. We also present photometric and spectroscopic evidence for a sixth lensed image of the same quasar. The maximum separation between the quasar images is 15.1. Both the large image separations and the high image multiplicity of the lensed quasar are in themselves exceptionally rare, and observing the combination of these two factors is an exceptionally unlikely occurrence in present datasets. This is only the third known case of a quasar lensed by a cluster, and the only one with six images. The lens system was discovered in the course of the Sloan Giant Arcs Survey, in which we identify candidate lenses in the Sloan Digital Sky Survey and target these for follow up and verification with the 2.56m Nordic Optical Telescope. Multi-band photometry obtained over multiple epochs from September 2011 to September 2012 reveal significant variability at the ~10-30% level in some of the quasar images, indicating that measurements of the relative time delay between quasar images will be feasible. In this lens system we also identify a bright (g = 21.5) giant arc corresponding to a strongly lensed background galaxy at z_s=2.30. We fit parametric models of the lens system, constrained by the redshift and positions of the quasar images and the redshift and position of the giant arc. The predicted time delays between different pairs of quasar images range from ~100 days to ~6 years.