  We report the superconducting properties of new hexagonal
Nb$_{10+2x}$Mo$_{35-x}$Ru$_{35-x}$Rh$_{10}$Pd$_{10}$ high-entropy alloys (HEAs)
(0 $\leq$ $x$ $\leq$ 5). With increasing $x$, the superconducting transition
temperature $T_{\rm c}$ shows a maximum of 6.19 K at $x$ = 2.5, while the
zero-temperature upper critical field $B_{\rm c2}$(0) increases monotonically,
reaching 8.3 T at $x$ = 5. For all $x$ values, the specific heat jump deviates
from the Bardeen-Cooper-Schreiffer behavior. In addition, we show that $T_{\rm
c}$ of these HEAs is not determined mainly by the density of states at the
Fermi level and would be enhanced by lowering the valence electron
concentration.
