Convert the logarithmic equation into exponential form. The statement log_5(x + 3) = 5 means x + 3 = 5^5. Now calculate 5^5 = 3125, so x + 3 = 3125. Subtract 3 from both sides: x = 3125 - 3 = 3122. Finally, check the domain: x + 3 must be positive, and 3122 + 3 = 3125 > 0, so the answer is valid.