In an effort to measure the masses of planets discovered by the NASA K2 mission, we have conducted precise Doppler observations of five stars with transiting planets. We present the results of a joint analysis of these new data and previously published Doppler data. The first star, an M dwarf known as K2-3 or EPIC 201367065, has three transiting planets (“b,” with radius 2.1 {R}\oplus ; “c,” 1.7 {R}\oplus ; and “d,” 1.5 {R}\oplus ). Our analysis leads to the mass constraints: {M}b={8.1}-1.9+2.0 {M}\oplus and M c < 4.2 M ⊕ (95% confidence). The mass of planet d is poorly constrained because its orbital period is close to the stellar rotation period, making it difficult to disentangle the planetary signal from spurious Doppler shifts due to stellar activity. The second star, a G dwarf known as K2-19 or EPIC 201505350, has two planets (“b,” 7.7 R ⊕ and “c,” 4.9 R ⊕) in a 3:2 mean-motion resonance, as well as a shorter-period planet (“d,” 1.1 R ⊕). We find M b = {28.5}-5.0+5.4 {M}\oplus , M c = {25.6}-7.1+7.1 {M}\oplus and M d < 14.0 M ⊕ (95% conf.). The third star, a G dwarf known as K2-24 or EPIC 203771098, hosts two transiting planets (“b,” 5.7 R ⊕ and “c,” 7.8 R ⊕) with orbital periods in a nearly 2:1 ratio. We find M b = {19.8}-4.4+4.5 {M}\oplus and M c = {26.0}-6.1+5.8 {M}\oplus . The fourth star, a G dwarf known as EPIC 204129699, hosts a hot Jupiter for which we measured the mass to be {1.857}-0.081+0.081 {M}{Jup}. The fifth star, a G dwarf known as EPIC 205071984, contains three transiting planets (“b,” 5.4 R ⊕ “c,” 3.5 R ⊕ and “d,” 3.8 R ⊕), the outer two of which have a nearly 2:1 period ratio. We find M b = {21.1}-5.9+5.9 {M}\oplus , M c < 8.1 {M}\oplus (95% conf.) and M d < 35 M ⊕ (95% conf.).