By exploiting two sets of high-resolution images obtained with HST ACS/WFC over a baseline of ~10 years we have measured relative proper motions of ~70,000 stars in the stellar system Terzan 5. The results confirm the membership of the three sub-populations with different iron abudances discovered in the system. The orbit of the system has been derived from a first estimate of its absolute proper motion, obtained by using bulge stars as reference. The results of the integration of this orbit within an axisymmetric Galactic model exclude any external accretion origin for this cluster. Terzan 5 is known to have chemistry similar to the Galactic bulge; our findings support a kinematic link between the cluster and the bulge, further strengthening the possibility that Terzan 5 is the fossil remnant of one of the pristine clumps that originated the bulge.
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