When brazing of heat-resistant nickel alloys (HSN) with traditional industrial brazing filler metals of the Ni−Cr−(B, Si) systems, the formation of brittle intermetallic compounds, namely, silicides and borides, occurs in the brazed seams. In order to prevent the formation of such undesirable brittle phases in brazed joints of heat-resistant nickel alloys, investigation is conducted using high-entropy alloys as brazing filler metals. This work shows the possibility of creating multicomponent high-entropy brazing filler metals based on the NiCoCrPdGe system, using calculation methods, binary state diagrams of metal systems and taking into account the classic Hume-Rothery solid-solution formation criteria. A number of thermodynamic parameters ($\Delta S_{m}$, $\Delta H_{m}$, $\delta$, $\Omega_m$, $VEC_{m}$) and the liquidus temperature are determined by calculation, and their corresponding dependences on the content of alloying components in the alloys of the NiCoCrPdGe system are constructed. The limiting range of alloying of experimental alloys is established, within which the values of these thermodynamic quantities correspond to the parameters applied to high-entropy alloys and contribute to the formation of a solid-solution structure with an f.c.c. lattice. Based on the obtained data, a section of the liquidus surface for the alloys of the NiCoCrPdGe system is plotted. According to the results of the conducted investigation, the limiting concentration limits of the depressant, namely, germanium, which ensure an acceptable melting temperature of the brazing filler metals when brazing heat-resistant nickel alloys, are determined. According to the results of experimental studies, it is established that the alloy of the NiCoCrPdGe$_{5}$ system is characterized by a two-phase dendritic structure. As determined by means of the calculation method, the volume fraction of the solid solution is of 72.54−75.47%.