A word for price after tax and service charge but before discount

Taken from here:

The net price is the price pre-tax, and the gross price should be the price including tax.

backed up by here:

you know a price after tax (the Gross price)
but want to find out the price before tax (the Net price).

So, I would say that :

$100 = initial price
$110 = Gross price
$100 = Net price.
$95 = Discount price
$105 = Total price

The first two answers above are not on point, the third is just wrong. The answer to the original question is a simple "Yes."

For the question, it doesn't matter how tax (or service charge) is calculated, we know it's $10. Similarly it doesn't matter whether the discount is applied before or after tax, we know it's $5.

According to the opening statement: The gross price is the price before deductions. The net price is the price after deductions [and, by the way, the price you pay].

Thus, exactly as posed: $100 -> initial price $110 -> gross price $105 -> net price [price paid]