About ten years ago, AACE recommended TSH range be adjusted to 0.3-3.0. Labs and doctors have been very slow to adopt that range. So, yes, yours is high, possibly indicating hypothyroidism.
Was TSH the only test done? TSH is a scrrening test at best, and an out-of-range TSH indicates the need for more testing, FREE T3 and FREE T4 (the actual thyroid hormones) should be tested, symptoms evaluated and decisions on whether to start meds based on those. Be sure to ask for FREE T3 and FREE T4, which are different and much more informative than total T3 and total T4..."free" must be specified or you'll get total.
My gyn said normal range is .3 to 5.0. So yours is a bit high.