The document outlines 5 major challenges of API testing: 1) Setting up the testing environment with the needed API parameters, 2) Sequencing API calls in the proper order, 3) Managing API versioning as systems evolve, 4) Addressing the near-infinite use cases of APIs, and 5) Validating parameters via API requests. It recommends adopting a modern API testing approach that utilizes leading tools for API testing automation and leverages experience testing applications at various layers to execute successful API testing.