Choice B is the correct answer. Rewrite with the same base and solve.

1. Rewrite: $25 = 5^2$, so $25 \cdot 5^x = 5^2 \cdot 5^x = 5^{x+2}$.
2. Equation: $5^{2x} = 5^{x+2}$.
3. Equal bases: Set exponents equal: $2x = x + 2$.
4. Solve: $2x - x = 2$, so $x = 2$.
5. Verify: $5^{2(2)} = 5^4 = 625$ and $25 \cdot 5^2 = 25 \cdot 25 = 625$ ✓

💡 Strategic Tip: When bases are equal, set exponents equal to solve.

Choice A is incorrect because$5^0 = 1$ and $25 \cdot 5^0 = 25$, not equal. Choice C is incorrect because$5^2 = 25$ and $25 \cdot 5 = 125$, not equal. Choice D is incorrect because$5^{-2} = 0.04$ and $25 \cdot 5^{-1} = 5$, not equal.