There has been an exponential growth in the number of low‐cost heterogeneous sensor devices that are connected to the internet in the existing infrastructure of smart cities in the past decade. These sensors and actuator devices are employed in various industries to collect invaluable data that greatly impacts business decisions. State‐of‐the‐art research is being carried out to process the high‐volume data collected in high velocity streams with high variability in order to draw meaningful insights to cater to business needs in various domains. Big data analytics finds diversified opportunities in 5G‐enabled Internet of Things (IoT) and industrial IoT environment to study the data patterns and produce new results which provides big organizations a conducive environment to take informed decisions. This article presents an exhaustive investigation of the various applications and algorithms of the big data analytics in 5G‐driven IoT and industrial IoT systems with a detailed taxonomy of the existing analytical systems and also the challenges specific to the applications in an IoT environment. A holistic understanding on the importance of security and privacy of big data during the development of smart city infrastructure in high velocity streaming process has been explained for a broad understanding of the big data streaming processes. A thorough analysis of important data mining algorithms such as classification, association rule mining, clustering, and prediction methods for big IoT data from the recent literature also has been presented to provide a clear understanding of existing issues in handling big data in 5G‐enabled IoT for the development of sustainable smart city infrastructure.