TM for $0^{5^n}$. Describing a turing machine that decides the language consisting of all strings of zeroes whose length is a power of 5
I'm gonna guess you're in s.datta's class?
I am not sure if this is correct but I tried to cross off 4 0's each time instead of 1.
It's like multiplying by 0.2 or the inverse operation of *5)

1*5 = 5
5*5 = 25
25*5 = 125 

125*0.2 = 25
25*0.2 = 5
5*0.2 = 1

Edit: formatting