What value of x satisfies 5^x+3 = 25^x-2?

Rewrite both sides with base 5. Since $25 = 5^2$, the right side is $(5^2)^{x-2} = 5^{2(x-2)}$. Equate exponents: $x + 3 = 2(x - 2) = 2x - 4$. Subtract $x$ and add 4: $7 = x$, choice D. Check: $5^{10}$ on the left and $25^5 = 5^{10}$ on the right. Choice A (1) gives $5^4$ versus $25^{-1}$. Choice B ($-1$) gives $5^2$ versus $25^{-3}$. Choice C (5) gives $5^8$ versus $25^3 = 5^6$. A common error is writing the right exponent as $2x - 2$, forgetting to distribute the 2 over both terms.