This may not be the most ellequent proof but actually you enumerate this easily. Because there are only 10 possibilities for last digit. You can write last digit for x^2 then for x^4 and finally x^5. Last digits upto 4:

x x^2 x^4 x^5

0 0 0 0

1 1 1 1

2 4 6 2

3 9 1 3

4 6 6 4

...

9 1 1 9

-O

Do not let the theory murder practice.