5G networks are envisioned to provide consumers and industry with improved transmission performance and advanced communication possibilities. To deliver on this promise of ushering in faster downloads and lower latency, mobile network operators are called upon for substantial investment in network infrastructure. Investors and operators need a clear 5G business case before making such investment. So far, very little research has been published on the topic of the 5G business case. This article studies the impact of different elements driving the business case of a 5G network. The study was performed within 3 boroughs of central London, UK, for the period 2020-2030. 5G-related costs and revenues were calculated to derive the business case. The results show that the business case for a 5G network providing mobile broadband services alone is positive over the time period 2020-2030 but has some risk in the later years of this time period. The business case is also particularly sensitive to assumptions on the revenue uplift and the rate of traffic growth which are inherently challenging to forecast. The sensitivity analysis shows that the return on investment becomes negative if both traffic and costs are significantly higher and revenues increase more slowly than our baseline forecasts. Network sharing helps to substantially improve the business case. Further research is needed to understand the business case on a regional or nationwide basis, and for a network that provides additional services beyond broadband.