We report the independent discovery and characterization of two K2 planets: K2-180b, a mini-Neptune-sized planet in an 8.9-d orbit transiting a V = 12.6 mag, metal-poor ([Fe/H] = -0.65 ± 0.10) K2V star in K2 campaign 5; K2-140b, a transiting hot Jupiter in a 6.6-d orbit around a V = 12.6 mag G6V ([Fe/H] = + 0.10 ± 0.10) star in K2 campaign 10. Our results are based on K2 time-series photometry combined with high-spatial resolution imaging and high-precision radial velocity measurements. We present the first mass measurement of K2-180b. K2-180b has a mass of Mp = 11.3 ± 1.9 M_{\oplus} and a radius of Rp = 2.2 ± 0.1 R_{\oplus}, yielding a mean density of ρp = 5.6 ± 1.9 g cm-3, suggesting a rocky composition. Given its radius, K2-180b is above the region of the so-called `planetary radius gap'. K2-180b is in addition not only one of the densest mini-Neptune-sized planets, but also one of the few mini-Neptune-sized planets known to transit a metal-poor star. We also constrain the planetary and orbital parameters of K2-140b and show that, given the currently available Doppler measurements, the eccentricity is consistent with zero, contrary to the results of a previous study.