5D action for longitudinal five branes on a pp-wave

String modes in a pp-wave background are generically massive, and the world-volume description of the branes is to be given by 'massive' gauge theories. In this paper, we present a five dimensional super Yang-Mills action with the Kähler-Chern-Simons term plus the Myers term as a low energy worldvolume description of the longitudinal five branes in a maximally supersymmetric pp-wave background. We derive the action from the M-theory matrix model on the pp-wave. We utilize the previously found 4/32 BPS solution of rotating five branes with stacks of membranes, but, to obtain the static configuration, we reformulate the matrix model in a rotating coordinate system which provides the inertial frame for the branes. Expanding the matrix model around the solution, we first obtain a non-commutative field theory action naturally equipped with the full sixteen dynamical supersymmetries. In the commutative limit, we show only four supersymmetries survive, resulting in a novel five dimensional "N = 1/2" theory.