  During this last decades, several attempts to construct slow invariant
manifold of the Lorenz-Krishnamurthy five-mode model of slow-fast interactions
in the atmosphere have been made by various authors. Unfortunately, as in the
case of many two-time scales singularly perturbed dynamical systems the various
asymptotic procedures involved for such a construction diverge. So, it seems
that till now only the first-order and third-order approximations of this slow
manifold have been analytically obtained. While using the Flow Curvature Method
we show in this work that one can provide the eighteenth-order approximation of
the slow manifold of the generalized Lorenz-Krishnamurthy model and the
thirteenth-order approximation of the "conservative" Lorenz-Krishnamurthy
model. The invariance of each slow manifold is then established according to
Darboux invariance theorem.
