The increasing demand for energy, rising electricity costs, and the growing need to reduce carbon emissions have driven industries toward the adoption of Renewable Energy Sources (RES) and Energy Storage Systems (ESS). However, selecting the most suitable ESS for industrial peak-shaving applications remains a complex decision involving technical, economic, and operational considerations. This paper proposes a practical and structured methodology for ESS selection that integrates conventional performance criteria with Industry 5.0 (I5.0) requirements, emphasizing sustainability, resilience, and human-centric industrial operation. Unlike existing multi-criteria decision-making approaches, the proposed framework reduces reliance on expert-based weighting, improving transparency and reproducibility. The methodology is implemented in two stages: initial KPI-based shortlisting of technologies, followed by detailed comparative performance analysis. A case study conducted in a European tire manufacturing plant compares lithium-ion batteries and flywheel energy storage systems under different peak-shaving strategies. Lithium-ion batteries demonstrated superior performance, covering approximately 80% of demand peaks compared with the 73% achieved by the flywheel system, confirming the effectiveness of the proposed methodology for practical industrial ESS selection.