Non-Orthogonal Multiple Access (NOMA) and caching are two proposed approaches to increase the capacity of future 5G wireless systems. Typically in NOMA systems, signals at the receiver are decoded using successive interference cancellation in order to achieve capacity in multi-user systems. The leveraging of caching in the physical layer to further improve on the benefits of NOMA is investigated, which is termed cache-aided NOMA. Specific attention is given to the caching cases where the users with weaker channel conditions possess a cache of the information requested by a user with a stronger channel condition. The probability that any of the users is in outage for any of the rates required for this NOMA system, defined as the union-outage, is derived for the case of fixed-power allocation, and the power allocation strategy that minimizes the union-outage probability is derived. Simulation results confirm the analytical results, which demonstrate the benefits of cache-aided NOMA on reducing the union-outages probability.