A quantum mechanical approach to the treatment of atom-penta-atom abstraction process of the type E+FABCD-->EF+ABCD is presented. The initial 12 degrees of freedom problem is simplified to a reaction having only 7 active degrees of freedom, emulating a rotating-stretching FABCD molecule. Its internal angles are frozen at their equilibrium values as the molecule collides with an attacking E atom. This model is then applied to the study of the H+CH4-->H2+CH3 reaction, predicting for the first time remarkable non-Arrhenius behavior. The dynamics was based on the Jordan and Gilbert analytical potential energy surface (JG-PES). The method employs the infinite-order-sudden-approximation (IOSA) method for the methane (CH4) rotations. Next, the coupled states (CS or j(z)) approximation is used to decouple the total angular momentum J from internal rotational operators. Finally, precessions are overcome by averaging the JG-PES around the out-of-plane angle in the attacking atom geometry. This treatment leads to a five-dimensional fully quantum mechanical computation for determining the total reaction probabilities, cross sections, and temperature-dependent rate constants. Comparing with experiment, the calculated rate constants show good agreement at high temperatures. At lower temperatures there are pronounced tunneling effects. A detailed comparison is made to other theoretical and experimental treatments.