This work presents a case study for the network planning of a 5G backhaul in a dense urban area. The study is fed by estimated population density data and real geographical layout coming from a Spanish city (Cartagena, around 220,000 population). The layout includes current locations of 4G base stations, which are assumed to place also new 5G macrocells, and real positions of lamp posts. The study assumes (i) an agreement among mobile operators to share the 5G network infrastructure, and (ii) a hypothetical agreement with the city hall, where the 5G deployment can be done by using city lamp posts for installing microcells, covering the city with a broadband 5G network outdoor access. An algorithm has been implemented to solve the dimensioning problem, as an Integer Linear Programming (ILP) technique. The deployment cost is proportional to the number of microcells to be installed in the study scenario. Results in terms of total number of microcells to be installed and traffic per microcell for different ratios of traffic demanded vs. traffic carried are also analysed. The results can help mobile network operators to drive their strategic investment decisions.