Carrier aggregation has been introduced by 3rd Generation Partnership project (3GPP) in order to meet the IMT-Advanced requirements. Using carrier aggregation, multiple component carriers with a different bandwidth, dispersed within intra or inter bands can be simultaneously utilised to provide higher data rates, better coverage and lower latency resulting a better user experience. However, carrier aggregation functionality requires modification to the radio resource management function of the network. In this paper, we propose an efficient resource allocation and link adaptation algorithm to support carrier aggregation functionality for downlink 5G LTE-Advanced (LTE-A) network. We consider a non-guaranteed bit rate bearers (best effort traffic), which can be used for non realtime applications such as file downloads. Most of the existing work considered resource allocation, component carrier selection and link adaptation as separate problems. We define a joint radio resource management problem with carrier aggregation functionality and propose a sub-optimal solution with a low computational complexity. Simulation results show clearly that our algorithm outperforms state-of-the-art algorithms.