Would TSH 5.4 and T4 7.6 be considered mild or severe? What test would my doctor have to do to know what caused my thyroid to be low?

Mild; repeat test. In most assays, the T4 is normal, and TSH slightly elevated. This could be nothing; sometimes a repeat test will come back normal. The question to ask: is your thyroid gland starting to fail? If so, it is early. Family history? Do you have symptoms? Positive anti-tpo antibodies? If you have symptoms and if there is evidence that your thyroid is failing, you should start on levothyroxine.