High-resolution measurements of the $K{\ensuremath{\alpha}}_{1,2}$ low-energy satellites were performed for the elements ${}_{42}$Mo, ${}_{44}$Ru, ${}_{46}$Pd, ${}_{48}$Cd, and ${}_{50}$Sn. The photoinduced x-ray spectra were measured using a high-resolution transmission-type bent-crystal spectrometer in modified DuMond slit geometry. Experimental evidence for the $K$-$\mathrm{LM}$ radiative Auger effect (RAE) in solid medium-mass atoms was found and particular groups of the $K$-$\mathrm{LM}$ RAE transitions were identified. The experimental intensity ratios $I(K$-$\mathrm{LM}$ RAE$)$ / $I(K{\ensuremath{\alpha}}_{1,2})$ as well as the relative intensity of the $K$-${L}_{3}{M}_{4,5}$ transition group were extracted from the measured spectra. A comparison of the experimental results with relativistic Hartree-Fock theoretical predictions from Scofield shows a good agreement. The experimental energies of the $K$-$\mathrm{LM}$ RAE edges are compared with calculated Auger transition energies.