After I lift weights, my muscles hurt too much to do it again for 4-5 days. I've heard 2-day recovery is normal. Am I doing something wrong?

I usually use the circuit machines, not free weights, and I do 3 sets of 15 reps (sometimes more on the 3rd rep, because I was told to keep going until I physically can't do one more rep).

For reference, I'm 25 y.o., 5'5, & 160 lbs.