Giving up gluten is not going to stop the Hashimoto's, but it will help you figure out which symptom is which. Gluten intolerance is NOT the same as Coeliac, although the symptoms are very alike. Gluten intolerance can give you the same symptoms as Hashi's so it is important for you to work out if giving up gluten is going to help you feel better in dealing with the Hashi's.
I gave up gluten many years ago and have Hashi. I know that eating any gluten (and barley and oats have gluten too, not just wheat) can make me tired, sluggish, vague and have memory loss. Hashi's does it too, but in a different way, and you can tell the difference.
Yes, gluten sensitivity is an autoimmune disease but not all Hashimoto patients have it. It can be good to give up gluten as the body really was never meant to eat wheat (which by evolution standards is a new comer grain to our diets.) It does NOT trigger an autoimmune disease, it is in itself an autoimmune disease and can not trigger others. That is not to say that people who already have gluten intolerance don't also have another autoimmune disease. Having one does not automatically procure another.
Having a TSH of 5 in many places would be regarded as hypo. You don't state what your antibodies you had were. Were they TPO and Tg antibodies? If so what were the numbers and reference ranges. See, having TPO antibodies is the one main test for Hashimoto's. You will become hypo and possibly hyper as the disease progresses.
Being on thyroid replacement is a good thing to help slow the process down.
Having your Free T3 and Free T4 tested is the best way of knowing how your body is dealing with the hormones of the thyroid, rather than the TSH which is just the pituitary sending out the message to make thyroid hormone IN the thyroid.
Confused yet? You should be! It is a complex disease and one that with a bit of learning you will get the hang of.
Cheers
Post your Free T3 and Free T4 Labs and TSH with reference ranges provided, members can advise and comment when we know where you are at with your thyroid. The symptoms you listed are Hypo. symptoms
although your MD should be going by Free T3 and Free T4 not TSH even with the old range, most have less symptoms with Tsh much lower. Good Luck FTB4