My sugars level reads btn 5-6mmol/dl even after exercise and my whole body feels shaky. Could this be normal or is my glucometer faulty?

Check the glucometer. You can check the glucometer- always good to do. The shakiness may be from a "drop" in the sugar level to which your body is not "accustomed" to. That's why it 's good to do gentle exercises and to advance slowly as tolerated. Be patient and gentle to yourself and you will succeed!