Hasti's disease in a man can cause low testosterone levels which can effect the sex drive. When hubby was Dx'ed in the fall the Endo told him he's probably going to need some testosterone replacement along with his thyroid medication. Blood test did confirm just that.
I'm not sure if other thyroid disease's can cause (I'm thinking so) low testosterone but a simple blood test could confirm that for you.
The AACE recommended a few years ago that the range for TSH be changed to 0.3-3.0; however, not all labs have done that; doctors merely look at the lab report and if you fall into the "normal" range, they are good to go; so your doctor is wrong that the proper range is 1-5. You are actually right at the top limit.
Have you had your Free T3 and Free T4 tested? Those are the actual thyroid hormones and need to be monitored along with TSH; after all, TSH is simply a "messenger" hormone from the pituitary telling the thyroid to make more hormone. TSH itself does not cause symptoms; it's the levels of FT3 and FT4 that cause or alleviate symptoms.
In addition to that, have you been tested for antibodies to rule out/confirm Hashimoto's thyroiditis? That's an autoimmune disease in which there are antibodies attacking/destroying the thyroid. Hashimoto's is the #1 cause for hypothyroidism.
I would suggest that you ask your doctor for the FT3, FT4, thyroid Peroxidase antibody (TPOab) and thyroglobulin antibody (TGab) tests. That will give a much clearer picture of what's going on.
If your doctor refuses to run these tests, I strongly suggest that you find another who will, because your doctor is actually keeping you sick by not knowing exactly what's going on (i.e. FT3/FT4 levels, etc).
Your hair loss should stop if your thyroid levels get right for you. I also believe that your sex drive should return. When we are so tired all the time, we just really don't want to do anything...........most of us have "been there, done that"........
Best of luck to you.