Even small elevations in TSH - 2.5 or higher - have been shown to increase cholesterol. The largest study to date on this issue (May 2007 issue of The Journal of Clinical Endocrinology & Metabolism) showed that treating such patients can lower cholesterol and LDL, improve function of the blood vessels, reduce obesity, and reduce fatigue. As far back as 2003, before much of the research on subclinical hypothyroidism emerged, the ATA claimed that it was up to the doctor and patient to decide whether patients with your TSH should be treated.
I have a TSH less than yours - I can certainly tell you, those symptoms are certainly familiar!
I had a TSH about 5.6 for years and was so, so sick. Get FT3, FT4 and another TSH. If your levels indicate hypothyroidism, you will benefit from Armour. In all liklihood, Armour would bring down your chol as well. It did mine. Have you considered estradiol? Some of your symptoms may be meno related.
A TSH of 5.8 is slightly abnormal and should be repeated about 6 weeks after the initial test -- it may be cause of dizziness and may be contributing to the inc'd cholesterol (but there may be other causes as well). Again, would repeat the TSH to make sure this wasn't just an unrelated transient abnormality.
I would certainly be dizzy with a high TSH of 5.8!!! I had vertigo very badly when at my hypothyroid worst. It did not go away on T4 meds only....when I took T3 meds all the head stuff went...including the vertigo. I would have different types...in the supermarket I would feel like the shelves were going to fall on me....other times it would be my head spinning....I couldn't stay in rooms with lines - like bathrooms with tiles or offices with wall panelling!!
I hope you're being treated for the hypothyroid??? If not you need some medication immediately!!