Recently, the 1/N_c expansion has been applied to the study of exotic baryons containing both quarks and antiquarks. We extend this approach to exotic states with mixed-symmetric spin-flavor symmetry, which correspond in the quark model to negative parity pentaquarks, and discuss the large N_c predictions for their mass spectrum. The heavy exotics Qq⁴ transform as 3,6,15 and 15′ under SU(3), while the light states qq⁴ include the exotic multiplets 10,27,35. We give mass relations among these multiplets in the 1/N_c expansion. In the quark model, the mass splittings between these states are given by color-spin interactions. Using the observation of an anticharmed exotic by the H1 Collaboration, we give predictions for the masses of other expected heavy pentaquarks.