1. **State the problem:** We are given that $3^x 5^y = 675$ where $x$ and $y$ are positive integers. We need to find the value of $x + y$. 2. **Prime factorize 675:** To solve for $x$ and $y$, first express 675 as a product of prime factors. $$675 = 3^3 \times 5^2$$ 3. **Match the powers:** Since $3^x 5^y = 3^3 5^2$, by comparing the exponents of the prime factors, we get: $$x = 3$$ $$y = 2$$ 4. **Calculate $x + y$:** $$x + y = 3 + 2 = 5$$ 5. **Answer:** The value of $x + y$ is 5, which corresponds to option (A).