In this study, the outage performance of a multi-relay cooperative network operating in a spectrum sharing environment is analysed. Focusing on the secondary communication process, a relay selection procedure is performed prior to the communication process, where the selected relay is the one maximising the instantaneous end-to-end signal-to-noise ratio (SNR) and, at the same time, satisfying the power restrictions imposed by the primary receivers. The secondary destination employs a selection combining strategy, selecting the best path (direct link or relaying link) with the highest instantaneous SNR. Two kinds of relaying protocols are considered: decode-and-forward and amplify-and-forward. For the former, an exact closed-form expression for the outage probability (OP) is derived, whereas for the latter an accurate approximation for the OP is obtained. Then, an asymptotic analysis is carried out and reveals that the system diversity order is N + 1 for both relaying protocols, with N denoting the number of relays. Monte Carlo simulations assess the accuracy of the authors' results.