In the equation \(C = 5 + 12x\), the coefficient of the term \(x\) is \(12\). This coefficient represents the rate at which Julia earns money for each additional hour she works at her pet-sitting job.
Therefore, the correct interpretation of the coefficient \(12\) in this context is:
Julia earns $12 an hour for her pet-sitting job.
The other options pertain to either the initial amount of money she has or the total earnings, which do not accurately describe the coefficient \(12\).