The theory of Realistic Mathematics Education (RME) is not merely a specific instructional method but rather a comprehensive educational perspective. It is founded upon profound insights into the nature of mathematics, the ways in which mathematics is learned, the role of reality in the process of knowledge construction, and a coherent system of characteristic pedagogical principles. From the viewpoint of RME, the Grade 5 mathematics curriculum holds significant potential for organizing learning activities that promote active student engagement through meaningful, context-based situations aligned with learners’ real-life experiences. This study proposes a teaching process grounded in the principles of Realistic Mathematics Education for Geometry and Measurement in Grade 5. The proposed process is developed based on an analysis of its pedagogical purposes and scientific underpinnings. Furthermore, the study illustrates this process through a sample learning activity designed to help students discover the formulas for calculating the lateral surface area and total surface area of a rectangular prism, as presented in the Vietnamese Grade 5 mathematics curriculum.