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From our analysis of six TESS sectors and a dedicated CHEOPS programme, we identify an inner planet (TOI-5788 b; $P = 6.340758\\pm 0.000030\\, d$) with radius $1.528\\pm 0.075\\, \\mathrm{R_{\\oplus }}$ and an outer planet (TOI-5788 c; $P = 16.213362\\pm 0.000026\\, d$) with radius $2.272\\pm 0.039\\, \\mathrm{R_{\\oplus }}$. We obtain 125 radial-velocity spectra from HARPS-N and constrain the masses of TOI-5788 b and c as $3.72\\pm 0.94\\, \\mathrm{M_{\\oplus }}$ and $6.4\\pm 1.2\\, \\mathrm{M_{\\oplus }}$, respectively. Although dynamical analyses indicate that a third planet could exist in a stable orbit between 8 and 14 d, we find no evidence of additional planets. Since the TOI-5788 system is one of the few systems with planets straddling the radius gap, and noting that there are even fewer such systems around metal-poor stars, it is a promising system to constrain planet formation theories. We therefore model the interior structures of both planets. We find that TOI-5788 b is consistent with being a rocky planet with almost no envelope, or having an atmosphere of a high mean molecular weight. We find that TOI-5788 c is consistent with both gas-dwarf and water-world hypotheses of mini-Neptune formation. We model the atmospheric evolution history of both planets. While both scenarios are consistent with the atmospheric evolution of TOI-5788 c, the gas-dwarf model is marginally preferred. The results of the atmospheric evolution analysis are not strongly dependent on stellar evolution. This makes the system a promising target to test internal structure and atmospheric evolution models.<\/jats:p>","DOI":"10.1093\/mnras\/stag158","type":"journal-article","created":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T12:57:52Z","timestamp":1769086672000},"source":"Crossref","is-referenced-by-count":0,"title":["Discovery and characterization of two exoplanets orbiting the metal-poor, solar-type star TOI-5788 with\n                    <i>TESS, CHEOPS<\/i>\n                    , and HARPS-N"],"prefix":"10.1093","volume":"546","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8122-2240","authenticated-orcid":false,"given":"Ben S","family":"Lakeland","sequence":"first","affiliation":[{"name":"School of Physics and Astronomy, University of Birmingham , Edgbaston, Birmingham B15 2TT ,","place":["UK"]},{"name":"Astrophysics Group, University of Exeter , Exeter EX4 2QL ,","place":["UK"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7254-4363","authenticated-orcid":false,"given":"A","family":"Mortier","sequence":"additional","affiliation":[{"name":"School of Physics and Astronomy, University of Birmingham , Edgbaston, Birmingham B15 2TT ,","place":["UK"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9140-3574","authenticated-orcid":false,"given":"R D","family":"Haywood","sequence":"additional","affiliation":[{"name":"Astrophysics Group, University of Exeter , Exeter EX4 2QL ,","place":["UK"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2417-7006","authenticated-orcid":false,"given":"S","family":"Ulmer-Moll","sequence":"additional","affiliation":[{"name":"Leiden Observatory, University of Leiden , Einsteinweg 55, NL-2333 CA Leiden ,","place":["the Netherlands"]},{"name":"Space Sciences, Technologies and Astrophysics Research (STAR) Institute, Universit\u00e9 de Li\u00e8ge , All\u00e9e du 6 Ao\u00fbt 19C, B-4000 Li\u00e8ge ,","place":["Belgium"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9483-2016","authenticated-orcid":false,"given":"Z","family":"Garai","sequence":"additional","affiliation":[{"name":"Astronomical Institute, Slovak Academy of Sciences , 059 60 Tatransk\u00e1 Lomnica ,","place":["Slovakia"]},{"name":"ELTE Gothard Astrophysical Observatory , Szent Imre h. u. 112, 9700 Szombathely ,","place":["Hungary"]}]},{"given":"A","family":"Vanderburg","sequence":"additional","affiliation":[{"name":"Center for Astrophysics | Harvard & Smithsonian , 60 Garden Street, Cambridge, MA 02138 ,","place":["USA"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1628-4231","authenticated-orcid":false,"given":"J A","family":"Egger","sequence":"additional","affiliation":[{"name":"Space Research and Planetary Sciences, Physics Institute, University of Bern , Gesellschaftsstrasse 6, CH-3012 Bern ,","place":["Switzerland"]},{"name":"European Space Agency (ESA), European Space Research and Technology Centre (ESTEC) , Keplerlaan 1, NL-2201 AZ Noordwijk ,","place":["the Netherlands"]}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-0867-9711","authenticated-orcid":false,"given":"D A","family":"Turner","sequence":"additional","affiliation":[{"name":"School of Physics and Astronomy, University of Birmingham , Edgbaston, Birmingham B15 2TT ,","place":["UK"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9137-9818","authenticated-orcid":false,"given":"D","family":"Kubyshkina","sequence":"additional","affiliation":[{"name":"Space Research and Planetary Sciences, Physics Institute, University of Bern , Gesellschaftsstrasse 6, CH-3012 Bern ,","place":["Switzerland"]},{"name":"Space Research Institute, Austrian Academy of Sciences , Schmiedlstrasse 6, A-8042 Graz ,","place":["Austria"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8946-8579","authenticated-orcid":false,"given":"A C M","family":"Correia","sequence":"additional","affiliation":[{"name":"University of Coimbra CFisUC, Department of Physics, , P-3004-516 Coimbra ,","place":["Portugal"]}]},{"given":"H P","family":"Osborn","sequence":"additional","affiliation":[{"name":"Center for Space and Habitability, University of Bern , Gesellschaftsstra\u00dfe 6, CH-3012 Bern ,","place":["Switzerland"]},{"name":"ETH Zurich , Department of Physics, Wolfgang-Pauli-Stra\u00dfe 2, CH-8093 Zurich ,","place":["Switzerland"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1605-5666","authenticated-orcid":false,"given":"L A","family":"Buchhave","sequence":"additional","affiliation":[{"name":"DTU Space, Technical University of Denmark , Elektrovej 328, DK-2800 Kgs. 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