ussr has it right. GT5 has auto-save turned on by default, but it will only trigger if you do certain actions like changing cars from your garage, finishing a race(or pitting during an enduro), when your timezone hits 12 midnight, and so forth. However, if you wish to change games without doing anything, the save button will save your progress as it stands.
After every save, it is advisable that you back up your data in case of corruption.