Structural, magnetic, transport, and thermal properties of ${\mathrm{YbCu}}_{5$-${}x}{\mathrm{Au}}_{x}$ alloys with Au concentration between $x=0.4$ (at the stability limit of ${\mathrm{AuBe}}_{5}$-type structure) and $x=0.7$ are reported. The outstanding features of this system are (i) the constant and record high value of ${C}_{m}/T$≈${}6.7$ J/mol ${\mathrm{K}}^{2}$ below a characteristic temperature ${T}^{*}$ (ranging between 150 mK and 350 mK), (ii) a power law of temperature dependence ${C}_{m}/T(T>{T}^{*})=g/{T}^{q}$, with $q$ ranging between 1.3 and 0.95 for decreasing $x$ from 0.7 to 0.5, and (iii) an observation of incoherent electronic scattering in the resistivity at $T<1$ K for $x$\le${}0.6$ despite the fact that Yb magnetic atoms are placed in an ordered lattice. Geometric frustration, originating from the tetrahedral distribution of Yb atoms, appears to be responsible for the lack of magnetic order and the exotic behavior of this system.