I'm pretty sure for all my multi night bookings using Hilton points in over 25 years all nights get charged at the same point rate. Yes, when paying money the rate can change each night but I've never seen a points rate change per night that I can remember.
Looking at your points used you are paying 240,000 for 5 nights (with 5th night free) which is 48,000 per night. If you add up the 5 individual nights if booked separately without a free night you would have paid 58,600 per night so you saved 53,000 points by booking them as 5 nights in one reservation instead of 5 separate reservations.