The possibility of superconductivity in tetragonal FeS has attracted considerable interest because of its similarities to the FeSe superconductor. However, all efforts made to pursue superconductivity in tetragonal FeS have failed so far, and it remains controversial whether tetragonal FeS is metallic or semiconducting. Here we report the observation of superconductivity at 5 K in tetragonal FeS that is synthesized by the hydrothermal reaction of iron powder with sulfide solution. The obtained samples are highly crystalline and less air-sensitive, in contrast to those reported in the literature, which are meta-stable and air-sensitive. Magnetic and electrical properties measurements show that the samples behave as a paramagnetic metal in the normal state and exhibit superconductivity below 5 K. The high crystallinity and the stoichiometry of the samples play important roles in the observation of superconductivity. The present results demonstrate that tetragonal FeS is a promising new platform to realize high-temperature superconductors.