So called fifth force is a concept which naturally emerges in the context of modern attempts to unify gravity with the other forces in nature. It represents an effective repulsive (anti-gravity) force which could balance out the normal attractive gravity force on galactic scales, and consequently, which could produce nearly flat rotation curves of spiral galaxies without need for dark matter. Fifth force also arises in the weak field limit of massive gravity theories and some Extended Theories of Gravity (ETG), in the form of a Yukawa-like correction to the Newtonian gravitational potential. Here we present a short overview of our investigations of possible influence of fifth force on the observed stellar orbits around the central supermassive black hole (SMBH) of our Galaxy. We fitted the simulated stellar orbits in Yukawa gravity into the observed orbits of several S-stars around Sgr A* at the Galactic Center (GC), and obtained the constrains on the parameters of Yukawa interaction which describe the intensity and the range of a fifth force. Assuming that the range of Yukawa interaction corresponds to the Compton wavelength of graviton, we also obtained an upper bound for graviton mass which was compatible with the value obtained by LIGO from gravitational-wave data. Taking into account that the GRAVITY Collaboration has recently measured the Schwarzschild precession in the orbit of S2 star and found that it was close to the prediction of General Relativity (GR), but with possible small deviations from it, we also studied whether these deviations could be caused by a fifth force. In such a case, we found that it is possible to use these discrepancies to further improve the constraints on the intensity and the range of a fifth force, as well as on upper bound for graviton mass.