I think "on""On" works better here. It implies that he died at some point on the 5th day of the treatment. I would use "at" to reference a very specific point in time (rather than a relatively longer period of time, such as a day), for example: "He died on the 5th day of the treatment at 3:02 PM".
See also: http://www.englishclub.com/grammar/prepositions-at-in-on-time.htm