Cooperative spectrum sharing systems (CSSSs) have recently received considerable attention from the wireless community due to their performance gains and spectrum utilization improvement when compared to traditional communication systems. Owing to this fact, we investigate the outage performance of CSSSs in the presence of multiple primary users (PUs). The secondary user (SU) network is composed by one source node, N decode-and-forward (DF) relays, and one destination. A best relay selection strategy is performed where the selected relay is that which maximizes the end-to-end signal-to-noise ratio (SNR) and, simultaneously, satisfies the interference constraint imposed by the MPU receivers. The communication between the SU source and SU destination is carried out through the help of one out of N DF relays and also via direct link. Afterwards, the SU destination selects the best path between the direct and the relaying path by using selection combining technique. A closed-form expression for the outage probability (OP) is derived, and an asymptotic analysis is carried out which reveals that the diversity order of the considered system equals N +1, showing that it is not affected neither by the number of PU receivers nor by the interference threshold. The presented analytical expressions are corroborated by means of Monte Carlo simulations and insightful discussions are provided.