To solve the equation, first express all terms with a common base, which is 5: $25 = 5^2$ and $625 = 5^4$. Rewriting the equation gives $5^{2(1-x)} \times 5^{x+2} \div 5^{-2x} = 5^{-4}$, simplifying to $5^{2 - 2x + x + 2 + 2x} = 5^{-4}$. Setting the exponents equal leads to the equation $2 + 2 = -4$, which simplifies to $x = -4$.