Convert the logarithmic equation into exponential form. The statement log_10(x + 7) = 5 means x + 7 = 10^5. Now calculate 10^5 = 100000, so x + 7 = 100000. Subtract 7 from both sides: x = 100000 - 7 = 99993. Finally, check the domain: x + 7 must be positive, and 99993 + 7 = 100000 > 0, so the answer is valid.