An old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542

We report the discovery of a 1.32$^{+0.10}_{-0.10}$ $\mathrm{M_{\rm Jup}}$ planet orbiting on a 75.12 day period around the G3V $10.8^{+2.1}_{-3.6}$ 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$^{+0.036}_{-0.035}$ $\mathrm{R_{\rm Jup}}$ and an insolation of 9.6$^{+0.9}_{-0.8}$ $S_{\oplus}$, 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] = $-$0.21$\pm$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 $\mathrm{M_{\rm Jup}}$ $$ 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.