Convert the logarithmic equation into exponential form. The statement log_5(x + 1) = 5 means x + 1 = 5^5. Now calculate 5^5 = 3125, so x + 1 = 3125. Subtract 1 from both sides: x = 3125 - 1 = 3124. Finally, check the domain: x + 1 must be positive, and 3124 + 1 = 3125 > 0, so the answer is valid.