  We report Very Large Array B-configuration observations of the atomic
hydrogen 21 cm line emission from the barred disk galaxy NGC 5597 at an angular
resolution of 7.1" x 4.2". Using the resonance method, and assuming the ratio
of the corotation radius to the semi-major axis of the stellar bar is unity
($\mathcal{R} \equiv R_{\rm CR}/a_{\rm bar} = 1$), we estimate the angular
pattern speed of the stellar bar to be, $\Omega_{{\rm bar}} \sim 15.3$ km
s$^{-1}$ kpc$^{-1}$. This constant value for $\Omega_{\rm bar}$ crosses
$\Omega_{\rm gas} + \kappa(R)/4$ at a distance $\sim 6.73$ kpc which would
correspond to the spatial location of the north spiral structure near an outer
m=4 resonance. This value of $\Omega_{\rm bar}$ is similar to the values
estimated for other bright nearby barred galaxies that exhibit circumnuclear
rings (near ILR) or outer rings (near OLR).
