Is a tsh of 5.13=hypothyroid.feel fatigued, low energy, slow resting heart rate, cold, anxiety/depression. 20 y.o.female.dr.didn't say it was abnormal?

If your TSH level is: within the normal range according to the laboratory's parameters, your MD will consider it normal. It is slightly high for some laboratories. If so, your doctor may order a Free T4 & Ultrasensitive TSH to determine if you have Hypothyroidism & if you need other studies & treatment. Either way, ask your MD for referral to mental health providers for diagnosis & management of anxiety/depression.