What are the last two digits of 5 to power of 347?

The answer is 25. The answer to any calculation 5n (for integer n>1) always ends with 25

The fact that computers cannot deal with large numbers and just add zeros at the end does not mean that the last two digits are actually zero. You can do the whole question modulo 100 and see that 5 to any power larger than 1 ends in 25.