We report the discovery of a 1.32(-0.10)(+0.10)M(Jup) planet orbiting on a 75.12 day period around the G3V 10.8(-3.6)(+2.1) Gyr old star TOI-5542 (TIC 466206508; TYC 9086-1210-1). The planet was first detected by the Transiting Exoplanet Survey Satellite (TESS) as a single transit event in TESS Sector 13. A second transit was observed 376 days later in TESS Sector 27. The planetary nature of the object has been confirmed by ground-based spectroscopic and radial velocity observations from the CORALIE and HARPS spectrographs. A third transit event was detected by the ground-based facilities NGTS, EulerCam, and SAAO. We find the planet has a radius of 1.009(-0.035)(+0.036)R(Jup) and an insolation of 9.6(-0.8)(+0.9)S(circle plus), along with a circular orbit that most likely formed via disk migration or in situ formation, rather than high-eccentricity migration mechanisms. Our analysis of the HARPS spectra yields a host star metallicity of [Fe/H] = -0.21 +/- 0.08, which does not follow the traditional trend of high host star metallicity for giant planets and does not bolster studies suggesting a difference among low- and high-mass giant planet host star metallicities. Additionally, when analyzing a sample of 216 well-characterized giant planets, we find that both high masses (4 M-Jup < M-p < 13 M-Jup) and low masses (0.5 M-Jup < M-p < 4 M-Jup), as well as both both warm (P > 10 days) and hot (P < 10 days) giant planets are preferentially located around metal-rich stars (mean [Fe/H] > 0.1). TOI-5542b is one of the oldest known warm Jupiters and it is cool enough to be unaffected by inflation due to stellar incident flux, making it a valuable contribution in the context of planetary composition and formation studies.