Convert the logarithmic equation into exponential form. The statement log_5(x + 2) = 4 means x + 2 = 5^4. Now calculate 5^4 = 625, so x + 2 = 625. Subtract 2 from both sides: x = 625 - 2 = 623. Finally, check the domain: x + 2 must be positive, and 623 + 2 = 625 > 0, so the answer is valid.