Are you allowed to take Part III of the exam January or June of your 5th year (granted you have 1040+ intern work hours)?

Yes, as long as those are paid intern hours that have occurred within a specified time frame. The hours cannot occur during weekends or evenings during the school year; they have to be either on winter or summer break. Also, they must be after you get your intern permit after the first professional pharmacy year. If all this is accomplished, then as long as you document them on the state form and have a notary and supervisor sign, then you should be good to go.