Using the property $a^n - b^n$ is divisible by $(a - b)$, $5^6 - 1$ is divisible by $(5^2)^3 - 1^3$, which is divisible by $5^2 - 1 = 24$, or $(5^3)^2 - 1^2$, divisible by $5^3 - 1 = 124$. Since $124 = 31 \times 4$, the expression is divisible by 31.