What is the sum of the tens digit and the ones digit of the integer form of $(2+3)^{23}$?
I want to find the tens digit and the ones digit of $(2+3)^{23}$, but I don't want to calculate the whole number, since it will be very large. I notice that the ones digit of any power of 5 is always 5, so the ones digit of $(2+3)^{23}$ is 5. To find the tens digit, I need to look at the last two digits of the powers of 5. I recall that the last two digits of the powers of 5 follow a pattern: 25, 25, 25, 25, ..., so the tens digit is always 2. Therefore, the sum of the tens digit and the ones digit of $(2+3)^{23}$ is 2 + 5 = 7. 