The integer −5 would best represent a situation where there is a loss or deficit. Let’s examine each event:
I. You gain 5 pounds. - This indicates a gain (which would be positive), not a loss. So, it does not represent −5.
II. You set your clock 5 hours ahead. - Setting the clock ahead does not represent a loss or negative amount, so it also does not correspond to −5.
III. You use 5 gallons of gas. - Using gas implies that you are losing gas, which can be represented as a negative quantity, corresponding to −5.
Based on this assessment, the only event that could be represented by the integer −5 is:
III only.
So, the correct answer is III only.