I have a tsh level of 0.05 but my t3 and t4 is normal. what is my problem?

Low tsh: A tsh of0.05 is very low and is consistent with hyperthyroidism in which case the t4 and t3 would be elevated. A tsh of 0.5 would be within normal limits. In cases of subclinical hyperthyroidism the tsh is low and the t4 and t3 are normal, as in your case. I recommend rechecking your tsh to be sure. A thyroidologist or endocrinologist is best to evaluate your situation if your tsh is still low.