if your Hba1c is 5.6 then your average blood sugar is around 120. Your fasting blood sugar is close to this. YOu are almost at the cutoff where you can be diagnosed as diabetic.
To address your blood sugar, the following are recommended:-
1. Losing weight if you are overweight (this will most easily happen on a lower carb diet).
2. Reduce processed foods in your diet, cut sugars, and eat lower carb. This will help greatly in managing blood sugars.
3. Exercise daily. Ideally 30 minutes or longer. If you can take a walk or other exercise after eating, this will also help.
4. Get a home blood sugar meter and test your sugars about 2 hours after eating. This number will tell you if what you ate raises your blood sugar or not. ideally your post eating results will be < 140 (even better if they are < 120 or close to 100).
5. You may ask your doctor to prescribe an insulin sensitizer drug such as metformin / Glucophage. This can be very useful for many.
Hope this helps.