Saving your progress in Yakuza 5 is straightforward but important. You can save your game at any phone booth scattered throughout the city districts. These are marked on your mini-map with a small phone icon. Simply approach a phone booth and press the interaction button (O/B) when prompted. You'll then be given the option to save your game to an available slot. It's highly recommended to save frequently, especially before major story missions, challenging boss fights, or after completing a significant number of substories.
While the game does feature some auto-save points, relying solely on them can lead to losing progress if you encounter an unexpected game over or need to quit abruptly. Always make a manual save at a phone booth to ensure your hard-earned progress is secure. There are plenty of phone booths in each city, so you're rarely far from a save point. Don't underestimate the importance of regular saving; it's a fundamental practice for any long RPG experience.