I had 1/2 my thyroid removed and my TSH went up to 5.3 and I had major weight gain in a month, bloated, couldn't walk, could barely think or talk.
Now after being on Synthroid 3 months, my TSH is .4. My endo said at that level my cholesterol may come down.
Currently accepted reference range for TSH is 0.3-3.0. Many labs still use obsolete ranges. So, yes, your TSH of 5.2 indicates hypothyroidism. It would also explain your symptoms. TSH is a pituitary hormone and not the best indicator of thyroid status. Make sure that your doctor is also testing free T3 and free T4 and basing his diagnosis and treatment on them rather than TSH.