Convert the logarithmic equation into exponential form. The statement log_3(x + 6) = 5 means x + 6 = 3^5. Now calculate 3^5 = 243, so x + 6 = 243. Subtract 6 from both sides: x = 243 - 6 = 237. Finally, check the domain: x + 6 must be positive, and 237 + 6 = 243 > 0, so the answer is valid.