What is the tens digit of $5^{2005}$?
I need to find the last two digits of $5^{2005}$, since the tens digit is the second-to-last digit. I notice that powers of 5 have a repeating pattern for their last two digits: 25, 25, 25, ..., no matter how high the exponent is. So I can conclude that the last two digits of $5^{2005}$ are also 25. Therefore, the tens digit is 2. 