Step 1 :The range is the difference between the highest and the lowest number in a set of numbers. In this case, we need to find the difference between the highest and the lowest number of hospitals in the five largest hospital systems.
Step 2 :The number of hospitals in the five largest hospital systems are \(340, 75, 123, 259, 151\).
Step 3 :The range of the number of hospitals is calculated as \(340 - 75 = 265\).
Step 4 :Final Answer: The range of the number of hospitals in the five largest hospital systems is \(\boxed{265}\).