Convert the logarithmic equation into exponential form. The statement log_5(x + 3) = 4 means x + 3 = 5^4. Now calculate 5^4 = 625, so x + 3 = 625. Subtract 3 from both sides: x = 625 - 3 = 622. Finally, check the domain: x + 3 must be positive, and 622 + 3 = 625 > 0, so the answer is valid.