Let's assume the total earnings before tax as x.
According to the given information, Rebecca must give 5 out of every x she earns to the tax department.
So, the amount she keeps after tax is (x - 5x/100) = (x - 0.05x) = 0.95x.
Given that Rebecca gets to keep $10 this week, we can set up the following equation:
0.95x = $10
Dividing both sides of the equation by 0.95:
x = $10 / 0.95
x ≈ $10.53
Therefore, the total amount she earned before tax this week is approximately $10.53.
Since none of the answer choices match this value, it seems there may be an error in the given information or answer choices.