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The launch of the 5th Generation (5G) mobile network allows for wireless communication at increased throughput rates and reduced latency compared to its predecessors and has opened for new possibilities in terms of computation offloading where demanding processes can be referred to powerful servers.User equipment (UE), i.e. wireless devices connected to a network, can benefit from offloading computational tasks to servers. Not only does it extend UE's computational resources, but also has the potential to reduce its energy consumption as it effectively redistributes the computational load to the server.This thesis is a study into the energy consumption trade-offs of this procedure for which a case study is done on a computer connected to a 5G network and tasked with the computation of a specific algorithm. Specifically, a comparison is made on the power consumption of computing the algorithm on the UE's central processing unit (CPU) and offloading it via a 5G modem, respectively, and a theoretical framework describing algorithms in terms of their utilization of these components is presented. By experimentally profiling the power consumption of the components and an algorithm's utilization thereof, these trade-offs can be quantified for a variety of signalling conditions. While the empirical study is a test case of a characteristic algorithm on a specific set of hardware components, the developed theoretical framework and methodology allows for the results to be extended to other hardware and algorithms, and general conclusions to be drawn on the energy consumption trade-offs in computation offloading. The results show that computation offloading is overwhelmingly beneficial in terms of power consumption and that the trade-offs only become comparable in certain edge cases. In particular, unless the CPU has an uncommonly low power consumption, the signal quality conditions are very poor or if the algorithm to be offloaded has a combination of low CPU load and high throughput requirements, offloading should always be considered a viable computational procedure in terms of energy consumption.