This work presents a comprehensive probabilistic margin assessment of the ASME BPVC primary load design rules for Class A components in Section III Division 5. This work evaluates the design margin of several of the Class A materials for a simple, but representative, component geometry across the entire Division 5 elevated temperature range. The margin assessment applies a probabilistic life prediction methodology developed in previous work that accounts for the variability in material strength and deformation. A Gaussian process fit captures the the strength variability, and a Monte Carlo approach accounts for the variability of steady-state creep deformation parameters leading to variability in the stresses developed in a component. A very efficient method based on the analogy between very viscous Stokes flow to steady-state creeping solid determines the steady-state stress distribution under primary load for the Monte Carlo approach. This work is therefore capable of efficiently evaluating the design margin of several materials across a wide range of temperatures. The probabilistic margin assessment presented in this work gives an insight into the design margin in the currently deterministic ASME Section III, Division 5 primary load design rules for high temperature nuclear components.