The acceptance criteria for a sprint focused on improving the performance of a system, like the one described for Sprint 5, typically include ensuring that the system meets specific performance benchmarks and that the functionality implemented in previous sprints continues to work as expected. Therefore, the most relevant acceptance criteria for such a sprint would be:

iii) "100% of the existing regression test suite has passed." This criterion ensures that the new performance enhancements have not adversely affected the existing functionalities of the system. It's a common practice in agile projects to maintain the integrity and quality of the system by running regression tests. This is supported by the notion that continuous testing and quality assurance are integral components of agile methodologies, ensuring that each increment of the project maintains and improves the quality of the product (Source: Agile Project Management methodologies).

iv) "System is responding in less than 3 seconds, 90% of the time." This criterion directly addresses the goal of the sprint, which is to increase the performance of the system. Setting a specific target for response times is a quantifiable and testable way to measure the improvement in performance. This aligns with agile principles, which emphasize delivering valuable, working software and encourage adaptive planning and continuous improvement. Performance targets like these help the team focus on delivering specific, valuable improvements to the system (Source: Principles behind the Agile Manifesto).

Options i) and v) are less relevant to the specific focus of Sprint 5, which is on performance improvement, and more about user roles and software compatibility, which are not directly tied to the performance objectives of the sprint. Therefore, options iii) and iv) constitute the most appropriate acceptance criteria for Sprint 5, focusing on ensuring that the system's performance meets the set benchmarks without compromising existing functionalities.