It's controversial.
The normal range for any lab test is determined as the 95% confidence interval for a sample of "young", "healthy" controls. Traditionally, that range for TSH has been ~0.5-5.0, though I've seen the ULN depending on the lab being anywhere from 4.5 to 6.0. The problem is that that 95% confidence interval is primarily grouped in the lower half of that range and determining "healthy" is difficult. If you rigorously screen your control population and exclude anyone with even a family hx of thyroid disease, you end up with a normal TSH range closer to 0.3-3.0, with that ULN being sometimes even as low as 2 or 2.5.
What to do with these intermediate TSH values (in the 2.5 to 5 or even 2.5 to 10 range) is something that if you ask three endocrinologists you'll get four opinions. Everyone is pretty certain that in pregnant women you should get the TSH < 2.5 in the first trimester and <3 thereafter (though the evidence on that is mixed as well), but for every other population it's really hard to say. Women of childbearing age I'll commonly start on LT4 to get them under 2.5. Anyone with clear symptoms is worth a trial of therapy as well, though clear symptoms is a nebulous thing to define (everyone is fatigued if you ask them often enough).
Other expert advised individuals to treat are those with a TSH above 10, those with a goiter, and those with positive antibodies. If you search for evidence supporting treatment in each of those cases, it's hard to get a clear answer. For a young person with these indications, I tend to err on the side of treatment.
The opposite problems happens with elderly individuals btw. The normal range is based on young people, but TSH tends to go up as you get older. So a TSH of 6 or 7 in an 85 year old might be perfectly normal, and it's even more controversial whether or not to treat them. Without clear symptoms, if a geriatric patient has a TSH <10, I typically avoid treating them.
Can also call on
@rokshana for another opinion.