  We present a complementary estimation of the critical exponent $\alpha$ of
the specific heat of the 5D random-field Ising model from zero-temperature
numerical simulations. Our result $\alpha = 0.12(2)$ is consistent with the
estimation coming from the modified hyperscaling relation and provides
additional evidence in favor of the recently proposed restoration of
dimensional reduction in the random-field Ising model at $D = 5$.
