If your 10th class marksheet was under the Central Board of Education (CBSE), then according to the Rules regarding Correction in Date of Birth, the application for correction in date of birth is to be forwarded by the Head of School along with documents mentioned in byelaws 69.2(iii). You can apply for the correction only within one year of the declaration of the result. You can fill the online form available at https://www.cbse.gov.in/newsite/dup.html. First you have to contact your school principal and then make an affidavit with the principalÕs signature stating that you want to correct the DOB from 1 July 1978 to 5 Aug 1979, and attach a copy of your birth certificate. Then you can send this affidavit to the CBSE Head Office. If they refuse to change the date of birth, you can approach the High Court under Article 226 and 227 of Constitution of India or Hon’ble Supreme Court under Article 32 of Constitution of India, to issue a writ of mandamus and direct the concerned school/board to make amendments to your certificate. This link contains the address, contact number and email ID of CBSE Regional offices https://www.cbse.gov.in/newsite/contact.html#reg. Contact them once before making the affidavit as process of application may differ from region to region.
Reference: Article 32, 226 and 227 of Constitution of India