The L5 Jupiter Trojan asteroids are minor bodies that orbit 60 degrees behind Jupiter. Because these orbits are stable over the lifetime of the Solar System, the properties of these objects may inform us about the conditions under which the Solar System formed. We present BVRKCIKC photometry for the 42 intrinsically brightest and presumably largest members of the L5 Jupiter Trojans. We define a new principal color component aT* that is indicative of taxonomic types relevant to the Jupiter Trojan asteroids. We find that 76% of the largest L5 Jupiter Trojans are consistent with a D-type classification, while 24% show shallower slopes more consistent with X-type and C-Type classifications. Such a breakdown is consistent with other surveys and will help to place the Trojans in the larger context of the Solar System.