In the framework of the color-magnetic interaction model, we have systematically calculated the mass splittings for the S-wave triply heavy pentaquark states with the configuration qqQQQ (Q = c, b; q = u, d, s). Their masses are estimated and their stabilities are discussed according to possible rearrangement decay patterns. Our results indicate that there may exist several stable or narrow such states. We hope the present study can help experimentalists to search for exotic pentaquarks. 16 3 Cnn Cnn = 30.0 K −16Cns K * 16 3 Ccs Cns = 18.7