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Abstract We present the discovery of a low-density planet orbiting the high-metallicity early M-dwarf TOI-5688 A b. This planet was characterized as part of the search for transiting giant planets (R ≳ 8R_⊕) through the Searching for Giant Exoplanets around M-dwarf Stars (GEMS) survey. The planet was discovered with the Transiting Exoplanet Survey Satellite, and characterized with ground-based transits from Red Buttes Observatory, the Table Mountain Observatory of Pomona College, and radial velocity (RV) measurements with the Habitable-Zone Planet Finder on the 10 m Hobby Eberly Telescope and NEID on the WIYN 3.5 m telescope. From the joint fit of transit and RV data, we measure a planetary mass and radius of 124 ± 24M_⊕(0.39 ± 0.07M_J) and 10.4 ± 0.7R_⊕(0.92 ± 0.06R_J), respectively. The spectroscopic and photometric analysis of the host star TOI-5688 A shows that it is a metal-rich ([Fe/H] = 0.47 ± 0.16 dex) M2V star, favoring the core-accretion formation pathway as the likely formation scenario for this planet. Additionally, Gaia astrometry suggests the presence of a wide-separation binary companion, TOI-5688 B, which has a projected separation of ~5″ (1110 au) and is an M4V, making TOI-5688 A b part of the growing number of GEMS in wide-separation binary systems.