The orbital motion of the transiting hot Jupiter TrES-5 b was reported to be perturbed by a planetary companion on a nearby orbit. Such compact systems do not frequently occur in nature, and learning their orbital architecture could shed some light on hot Jupiters' formation processes. We acquired fifteen new precise photometric time series for twelve transits of TrES-5 b between June 2019 and October 2020 using 0.9-2.0m telescopes. The method of precise transit timing was employed to verify the deviation of the planet from the Keplerian motion. Although our results show no detectable short-time variation in the orbital period of TrES-5 b and the existence of the additional nearby planet is not confirmed, the new transits were observed about two minutes earlier than expected. We conclude that the orbital period of the planet could vary in a long timescale. We found that the most likely explanation of the observations is the line-of-sight acceleration of the system's barycentre due to the orbital motion induced by a massive, wide-orbiting companion.