We present the results of our search for a dynamical family around the active asteroid P/2012F5 (Gibbs). By applying the hierarchical clustering method, we discover an extremely compact 9-body cluster associated with P/2012F5. The statistical significance of this newly discovered Gibbs cluster is estimated to be >99.9%, strongly suggesting that its members share a common origin. The cluster is located in a dynamically cold region of the outer main-belt at a proper semi-major axis of about 3.005 AU, and all members are found to be dynamically stable over very long time-scales. Backward numerical orbital integrations show that the age of the cluster is only 1.5 $pm$ 0.1 Myr. Taxonomic classifications are unavailable for most of the cluster members, but SDSS spectrophotometry available for two cluster members indicate that both appear to be $Q$-type objects. We also estimate a lower limit of the size of the parent body to be about 10 km, and find that the impact event which produced the Gibbs cluster is intermediate between a cratering and a catastrophic collision. In addition, we search for new main-belt comets in the region of the Gibbs cluster by observing seven asteroids either belonging to the cluster, or being very close in the space of orbital proper elements. However, we do not detect any convincing evidence of the presence of a tail or coma in any our targets. Finally, we obtain optical images of P/2012F5, and find absolute R-band and V-band magnitudes of $H_R$ = 17.0 $pm$ 0.1 mag and $H_V$ = 17.4 $pm$ 0.1 mag, respectively, corresponding to an upper limit on the diameter of the P/2012F5 nucleus of about 2 km.
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