Hi....My fasting blood sugar is 5.54mmol/l. I have also done hba1c test and the result is 5.0%. I need your kind suggestions?

Diabetes. If your hemoglobin a 1c is 5 then do not worry you are not diabetic however if you have a family history of diabetes you have to check your blood sugar and hemoglobin a1c more frequently.
See below. Hba1c is the averaging of the blood sugar 24/7 for the last 90 days. Yours of 5.0 is borderline elevated by earlier criteria. Your FBS is also on the high side of normal. Weight control, regular aerobic exercise 3 times/week+, avoiding a diet high in fats and simple sugars will slow/stop progression. Aim for ideal body weight.