Last digit of fifth powers

Statement

One can prove $n^5\equiv n\pmod{10}$ for every integer $n$, i.e. a fifth power ends in the same digit as its base. Verify it for $n=7$ by finding the last digit of $7^5$.

Solution

$7^5=16807,$ whose last digit is $\boxed{7}$, the same as the base $7$. This agrees with $n^5\equiv n\pmod{10}$.