Verified answer

There's extra information here. An "average rate of change" is just (the amount of the change) divided by (elapsed time). The amount of change is given as -7,727.5 ft, and the time as 5 minutes, so just compute:

rate = (-7,725.5 ft) / (5 min.) = -1,545.5 ft/min.

You didn't need the original altitude.

PS: If the rate in ft/sec is required, you can repeat the rate calculation using 300 sec. instead of 5 min. (...or just divide the above answer by 60.)