To find the change in the amount of water being removed from the fire engine's hose each minute, we start by determining the rate at which water is being removed.
The pump removes 250 gallons every 5 minutes. We can calculate the rate per minute by dividing the total gallons removed by the number of minutes:
\[ \text{Rate per minute} = \frac{250 \text{ gallons}}{5 \text{ minutes}} = 50 \text{ gallons per minute} \]
Since the pump is removing water, the change in the amount of water in the hose is negative:
\[ \text{Change in amount of water per minute} = -50 \text{ gallons per minute} \]
Thus, the change in the amount of water in gallons each minute is \(-50\) gallons.