Step 1 :The distance at 2:00 is 163 miles and the distance at 5:00 is 351 miles.
Step 2 :The total distance traveled from 2:00 to 5:00 is calculated by subtracting the distance at 2:00 from the distance at 5:00, which is \(351 - 163 = 188\) miles.
Step 3 :The total time from 2:00 to 5:00 is 3 hours.
Step 4 :The average speed is calculated by dividing the total distance traveled by the total time, which is \(\frac{188}{3} = 62.67\) miles per hour.
Step 5 :Final Answer: The average speed from 2:00 to 5:00 is \(\boxed{62.67}\) miles per hour.