|We consider an autonomous system of ordinary
differential equations, which is solved with respect to derivatives. To
study local integrability of the system near a degenerate stationary
point, we use an approach based on Power Geometry method and on the
computation of the resonant normal form. For a planar 5-parametric
example of such system, we found the complete set of necessary and
sufficient conditions on parameters of the system for which the system
is locally integrable near a degenerate stationary point.