Convert the logarithmic equation into exponential form. The statement log_4(x + 4) = 5 means x + 4 = 4^5. Now calculate 4^5 = 1024, so x + 4 = 1024. Subtract 4 from both sides: x = 1024 - 4 = 1020. Finally, check the domain: x + 4 must be positive, and 1020 + 4 = 1024 > 0, so the answer is valid.