Intrusion detection systems (IDSs) for 5G networks must handle complex, high-volume traffic. Although opaque "black-box" models can achieve high accuracy, their lack of transparency hinders trust and effective operational response. We propose ExAI5G, a framework that prioritizes interpretability by integrating a Transformer-based deep learning IDS with logic-based explainable AI (XAI) techniques. The framework uses Integrated Gradients to attribute feature importance and extracts a surrogate decision tree to derive logical rules. We introduce a novel evaluation methodology for LLM-generated explanations, using a powerful evaluator LLM to assess actionability and measuring their semantic similarity and faithfulness. On a 5G IoT intrusion dataset, our system achieves 99.9\% accuracy and a 0.854 macro F1-score, demonstrating strong performance. More importantly, we extract 16 logical rules with 99.7\% fidelity, making the model's reasoning transparent. The evaluation demonstrates that modern LLMs can generate explanations that are both faithful and actionable, indicating that it is possible to build a trustworthy and effective IDS without compromising performance for the sake of marginal gains from an opaque model.

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