  We report resonant inelastic X-ray scattering (RIXS) measurements on ordered
double perovskite samples containing Re$^{5+}$ and Ir$^{5+}$ with $5d^2$ and
$5d^4$ electronic configurations respectively. In particular, the observed RIXS
spectra of Ba$_2$YReO$_6$ and Sr$_2$MIrO$_6$ (M=Y, Gd) show sharp
intra-t$_{2g}$ transitions, which can be quantitatively understood using a
minimal `atomic' Hamiltonian incorporating spin-orbit coupling ($\lambda$) and
Hund's coupling ($J_H$). Our analysis yields $\lambda=0.38(2)$eV with
$J_H=0.26(2)$eV for Re$^{5+}$, and $\lambda=0.42(2)$eV with $J_H=0.25(4)$eV for
Ir$^{5+}$. Our results provide the first sharp estimates for the Hund's
coupling in $5d$ oxides, and suggest that it should be treated on equal footing
with spin-orbit interaction in multi-orbital $5d$ transition metal compounds.
