Attempts to prepare Gd$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$Co$\mathrm{<mrow\; data-mjx-texclass="ORD">5</mrow>}$Bi, a member of the rare-earth (RE) intermetallics RE$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$Co$\mathrm{<mrow\; data-mjx-texclass="ORD">5</mrow>}$Bi, which were identified by a machine-learning recommendation engine as potential candidates for thermoelectric materials, led instead to formation of the new compound Gd$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$Co$\mathrm{<mrow\; data-mjx-texclass="ORD">5.3</mrow>}$Bi with a very similar composition. Phase equilibria near the Gd-rich corner of the Gd-Co-Bi phase diagram were elucidated by both lab-based and variable-temperature synchrotron powder X-ray diffraction, suggesting that Gd$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$Co$\mathrm{<mrow\; data-mjx-texclass="ORD">5.3</mrow>}$Bi and Gd$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$Co$\mathrm{<mrow\; data-mjx-texclass="ORD">5</mrow>}$Bi are distinct phases. The higher symmetry structure of Gd$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$Co$\mathrm{<mrow\; data-mjx-texclass="ORD">5.3</mrow>}$Bi (cubic, space group Im3̅, Z = 2, a = 9.713(6) Å), as determined from single-crystal X-ray diffraction, is closely related to that of Gd$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$Co$\mathrm{<mrow\; data-mjx-texclass="ORD">5</mrow>}$Bi (tetragonal, space group Immm). Single Co atoms and Co-Co dumbbells are disordered with occupancies of 0.78(2) and 0.22(2), respectively, in Gd$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$Co$\mathrm{<mrow\; data-mjx-texclass="ORD">5.3</mrow>}$Bi, but they are ordered in Gd$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$Co$\mathrm{<mrow\; data-mjx-texclass="ORD">5</mrow>}$Bi . Consistent with this disorder, the electrical resistivity shows less dependence on temperature for Gd$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$Co$\mathrm{<mrow\; data-mjx-texclass="ORD">5.3</mrow>}$Bi than for Gd$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$Co$\mathrm{<mrow\; data-mjx-texclass="ORD">5</mrow>}$Bi . The thermal conductivity is low and reaches 2.8 W m$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ K$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ at 600 °C for both compounds; however, the temperature dependence of the thermal conductivity differs, decreasing for Gd$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$Co$\mathrm{<mrow\; data-mjx-texclass="ORD">5.3</mrow>}$Bi and increasing for Gd$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$Co$\mathrm{<mrow\; data-mjx-texclass="ORD">5</mrow>}$Bi as the temperature increases. The unusual trends in thermal properties persist in the heat capacity, which decreases below 2R, and in the thermal diffusivity, which increases at higher temperatures.