TSH=5.44 is horrible. Should be closer to 1.0
Thyroid ranges are stupid wrong.
What other thyroid labs?
* fT3 - this is the active hormone
* thyroid autoimmune panel
The best outcome would be if this was caused by your not using iodize salt, which can be fixed, but there can be complications from high TSH+years.
With this thyroid problem, you will not feel well even if TRT is otherwise perfect.
Read all of the thyroid basics sticky.
Evaluate your overall thyroid function by checking oral body temperatures as per the thyroid basics sticky. Thyroid hormone fT3 is what gets the job done and it regulates mitochondrial activity, the source of ATP which is the universal currency of cellular energy. This is part of the body's temperature control loop. This can get messed up if you are iodine deficient. In many countries, you need to be using iodized salt. Other countries add iodine to dairy or bread.