Find the sum of the distinct prime factors of $5^5 - 5^3$.
I notice that the expression $5^5 - 5^3$ has a common factor of $5^3$, so I can factor it out as $5^3(5^2 - 1)$. This makes it easier to find the prime factors, since I already know that $5^3$ is a prime power. To find the prime factors of $5^2 - 1$, I can use the difference of squares formula and write it as $(5 - 1)(5 + 1)$, which is $4 \times 6$. I know that $4$ and $6$ are not prime, so I can further factor them as $2^2 \times 2 \times 3$. Now I have $5^5 - 5^3 = 5^3 \times 2^2 \times 2 \times 3$. The distinct prime factors are $5$, $2$, and $3$, and their sum is $5 + 2 + 3 = 10$. 