I want to be clear.
First of all. Cytomel is usually measured in MICRO-grams or mcg. You listed 5 Mg. Which would be 5,000 micro grams (mcg)
Secondly. Is the Dr. recommending that you take the 5 mcg three times a day which would equal 15 mcg per day?
If so that is a LOT of T3 to take if you have not worked your way up to that level. Many people cannot handle going from zero T3 to 15 mcg per day without some amount of time to work up to it.
15 mcg is not unheard of by any means. However like I said it is really a big jump to do directly to.
You have given no information as to what your FT4 and FT3 levels currently are, and what symptoms you have. So it is really hard to determine if the direction and dosage is reasonable without this additional information to help provide the best advice.
Be aware that in spite of what many doctors will tell you, your thyroid status of being either hypothyroid, euthyroid or hyperthyroid is not defined by a TSH test. Your thyroid status is primarily defined by symptoms, along with levels of the biologically active thyroid hormones, Free T4 and Free T3 (not the same as Total T4 and Total T3).
Your new med dosages are well within normal amounts, and unlikely to cause hyper symptoms. For further confirmation of that we need to know more about your history of diagnosis and treatment. If tested for Free T4 and Free T3, please post those results along with reference ranges shown on the lab report. Also please tell us about the diagnosed cause for your hypothyroidism. What symptoms do you have currently, if any? Why did the doctor decide to add the Cytomel?