So the correct date of birth is April 10, 1980 but the baptismal record says May 13, 1980. Am I understanding you properly?
If so, you should only need to contact the office of the parish where the baptism took place and tell the person in charge of records that it’s wrong. You may need to provide official proof of this, such as a government-issued birth certificate.
How the correction is noted in the sacramental record, I can’t tell you. In my parish, a recent record would simply be corrected in each of the two identical registers. If the baptism took place long enough in the past that one of the registers has already been sent to the diocesan archive, however, the process is problem different but I couldn’t tell you what it is. And each parish may have different procedures in place. Your best bet is to ask the parish of record for the baptism.