5^1=5
5^2=25
5^3=125
using patterns determine the last 3 digits of 5^100
doing a few more ...
5^4 = 625
5^5 = 3125
5^6 =15625
5^7 = 78125
5^8 = 390625
looks like the last 3 digits alternate 125 and 625
for an odd exponent they are 125 and for an even exponent they are 625
So what do you think?