Here's a "proof"
5^2 = 25
5^3 = 25 * 5 = (20 + 5) (5) = 100 + 25
5^4 = 125 * 5 = (120 + 5) (5) = (100 + 20 + 5) (5) = 500 + 100 + 25
5^5 = 625 * 5 = (600 + 20 + 5) (5) = (500 + 100 + 25)(5) = (500 + 100 + 20 + 5) (5) = 2500 + 500 + 100 + 25
So it appears that the pattern for 5^n =
25 + 100*5^(0) + 100*5^(1) +.....+ 100*5^(n - 4) + 100*5^(n- 3) for n ≥ 5
And, in this series, all terms except the first one will end in the digits "00"...so adding 25 to this sum will always result in a number ending in "25"..........
