This paper presents performance evaluations for two Spectrum-Sharing cognitive-radio systems employing cooperative amplify-and-forward relaying in which the best relay is selected for the transmission. In these systems, a secondary user (SU, unlicensed user) shares the Spectrum of a primary user (PU, licensed user), in such a way that the interference to the PU is always kept below a predefined threshold. To this end, a power control for the SU is used. In these systems, the SU employs an amplify-and-forward relaying with several relays, where the best relay who has the best channel condition is selected for the transmission. The considered systems are different in the employed relay selection schemes, such that: 1) In the first system, partial relay selection is employed, in which the partial channel state information (CSI) is used to select the best relay. 2) In the second system opportunistic relay selection is employed, in which the full CSI is used to select the best relay. To analyze the system performances, at first the cumulative distribution function (CDF) of the received signal-to-noise-ratio (SNR) for each considered system is derived. Then, using the obtained CDF expressions, closed-form expressions are obtained for three performance metrics: outage probability, the average bit-error-rate (BER), and the average channel capacity. Finally, using the numerical results obtained from the mathematical formulas derived in this paper, we evaluate and compare the systems performances in different cases under different conditions. In addition, to verify the accuracy of the performed analysis, Monte-Carlo simulation results are also provided.