The hotel reservation is for the number of nights that you need the room. If you use the first, the 1st THROUGH the 5th, one might assume you want to stay 6 nights and leave on the 6th, and if you use the second, the 1st TO the 5th, that you would leave on the 5th, staying only 5 nights. Therefore, since this in unclear and you and the person making the reservation want to be absolutely clear, you should be sure to state the date you will ARRIVE and the date that you will DEPART or LEAVE. Then you are sure to have the right dates. Even when I speak in English and speak to an English speaker to reserve a room, I always have them repeat the dates to arrive and depart.