Thank you for your query at DoctorSpring.com
Hb A 1c is a reflection of the blood sugar levels in your body over the preceding 3 months. Your values of 5.6 come in the normal range and therefore I would like to firstly reassure you that your physician is correct in saying that you shoukd not worry.
An A1C level of 5.7 to 6.4 is called pre-diabetes, a value above 6.5 is diabetes. According to guidelines, physicians begin to treat HB A1C levels of more than 7 with anti-diabetes medication, but only after a trial of diet and liefstyle modification.
Therefore, despite your family history of diabetes, your current HB A1C level is normal.
Hope this helps, feel free to reply with any further queries that you may have,