The radiative proton-capture reactions Ne19(p,γ)Na20, Mg23(p,γ)Al24, Si27(p,γ)P28, S31(p,γ)Cl32, and Ar35(p,γ)K36 potentially influence energy generation and/or nucleosynthesis during explosive hydrogen burning in classical novae and/or type I x-ray bursts. The thermonuclear rates of these reactions are dependent on resonance energies Er=Ex-Q and strengths ωγ. The Ne20(He3,t)Na20, Mg24(He3,t)Al24, Si28(He3,t)P28, S32(He3,t)Cl32, and Ar36(He3,t)K36 reactions have been measured using a 32-MeV, He32+ beam; ion-implanted carbon-foil targets developed at the University of Washington; and the Munich Q3D magnetic spectrograph. This experiment has already yielded precision mass measurements of Na20, Al24, P28, and Cl32 [C. Wrede , Phys. Rev. C 81, 055503 (2010)]PRVCAN0556-281310.1103/PhysRevC.81.055503, which are used presently to constrain the corresponding (p,γ) reaction Q values. The new Al24 and P28 masses resolve a discrepancy in the energy of the lowest-energy resonance in the Mg23(p,γ)Al24 reaction and better constrain a direct measurement of its strength. Excitation energies in Cl32 and K36 have also been measured. An important new proton-unbound level has been found at Ex=2196.9(7) keV in K36 and the uncertainties in K36 excitation energies have been reduced by over an order of magnitude. Using the new data on K36, the A=36, T=1 triplets have been reassigned. The thermonuclear Ar35(p,γ)K36 reaction rate is found to be much higher than a commonly adopted rate and this could affect energy generation in type I x-ray bursts.