Large Language Models (LLMs) have become essential in a variety of applications due to their advanced language understanding and generation capabilities. However, their computational and memory requirements pose significant challenges to traditional hardware architectures. Processing-in-Memory (PIM), which integrates computational units directly into memory chips, offers several advantages for LLM inference, including reduced data transfer bottlenecks and improved power efficiency. This paper introduces PIM-AI, a novel DDR5/LPDDR5 PIM architecture designed for LLM inference without modifying the memory controller or DDR/LPDDR memory PHY. We have developed a simulator to evaluate the performance of PIM-AI in various scenarios and demonstrate its significant advantages over conventional architectures. In cloud-based scenarios, PIM-AI reduces the 3-year TCO per queries-per-second by up to 6.94x compared to state-of-the-art GPUs, depending on the LLM model used. In mobile scenarios, PIM-AI achieves a 10- to 20-fold reduction in energy per token compared to state-of-the-art mobile SoCs, resulting in 25 to 45~\% more queries per second and 6.9x to 13.4x less energy per query, extending battery life and enabling more inferences per charge. These results highlight PIM-AI's potential to revolutionize LLM deployments, making them more efficient, scalable, and sustainable.