Remember what we have got here, I'll use it twice (for 2 and for 3).
Now let's take out the 2's from it.
Because $5^n - 5^k$ is even and therefore $5^n - 5^k +1$ is odd, $(5^2- 5+1), (5^6- 5^3 +1), (5^4 - 5^2 +1), (5^{12} -5^6 +1)$ obviously can't be divided by 2.
So we are left with