1. **State the problem:** Solve for $x$ in the equation $$10^3 \cdot 10^x \cdot 10^2 = 10^5.$$\n\n2. **Recall the rule for multiplying powers with the same base:** When multiplying powers of 10, add the exponents: $$10^a \cdot 10^b = 10^{a+b}.$$\n\n3. **Apply the rule to the left side:** $$10^3 \cdot 10^x \cdot 10^2 = 10^{3+x+2} = 10^{x+5}.$$\n\n4. **Set the exponents equal since the bases are the same:** $$x + 5 = 5.$$\n\n5. **Solve for $x$:** $$x + 5 = 5 \implies x = 5 - 5 = 0.$$\n\n**Final answer:** $$x = 0.$$