5.45 isn't all that high. The norm is .40-4.5. Mine is 5.66 right now but is high enough to give me symptoms that my meds are off. Every few years my meds need to be adjusted. (I've actually been without a thyroid gland since 1990)
Are you having any of the other symptoms, like puffiness, dry skin and hair, trouble sleeping at night, or cold all the time? And, of course, gaining weight? If so, maybe you should find an endo guy and talk to him.