1. **State the problem:** Simplify the expression $$5^{2x+3} \cdot 5^{x-5}$$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying powers with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$ 3. **Apply the rule:** $$5^{2x+3} \cdot 5^{x-5} = 5^{(2x+3) + (x-5)}$$ 4. **Simplify the exponent:** $$5^{2x+3+x-5} = 5^{3x - 2}$$ 5. **Final answer:** $$5^{3x - 2}$$