Convert the logarithmic equation into exponential form. The statement log_5(x + 7) = 4 means x + 7 = 5^4. Now calculate 5^4 = 625, so x + 7 = 625. Subtract 7 from both sides: x = 625 - 7 = 618. Finally, check the domain: x + 7 must be positive, and 618 + 7 = 625 > 0, so the answer is valid.