1. **State the problem:** Solve the equation $2^3 = 2^5$. 2. **Recall the rule for exponents:** If $a^m = a^n$ and $a \neq 0$, then $m = n$. 3. **Apply the rule:** Since the bases are the same (2), set the exponents equal: $$3 = 5$$ 4. **Evaluate:** This is a contradiction because 3 does not equal 5. 5. **Conclusion:** The equation $2^3 = 2^5$ is false; there is no solution where the exponents are equal. Therefore, the original equation is not true.