Birth date in birth certificate and school record differs by 5 days.  How to resolve?

Admission to primary school demanded that the ward should be 5 years age as on 1st june.  My son was born on 7th june and to satisfy the above requirement, so that he won’t lose a year, he was admitted to school with date of birth as 1st june (no birth certificate was mandatory for admission to school then!). However, for issuance of passport, it is necessary that both birth certificate and school admission extract be submitted.  Obviously the dates differ.  Changing school records birth date to match actual birth date is an unimaginably cumbersome procedure.  Since the difference is only few days, would it be ok to own up the error (with explanation why it was done, etc.) and request the passport officer to issue passport as per the school records?  An undertaking can also be given that no other passport request with the actual birth date will be submitted ever.  Since the Passport office’s interest is to ensure that the person does not apply for another passport with a different birth date, is it not within Passport Officer’s discretion to issue the passport as requested, especially in the light of admission of gilt and undertaking not to ever request a passport with actual birth date?  I would appreciate opinion of the legal fraternity on this matter.  I am being honest in admitting a mistake and requesting condonation – if there is a penalty for the mistake, I am willing be punished too!