Dar-es-Salaam is in the south and Kilmanjaro in the north.
It takes up most the day to travel by bus to Arusha from Dar-es-Salaam, so unless you fly, 2 days will be taken up by travelling there and back
Kilimanjaro is not near the Northern Route safari parks and from Tanzania you can not get a good view of the mountain - this is best viewed from Amboselli in Kenya.
It is a long drive from Arusha to Northern Route safari parks of Tangire, Ngorongoro Crater and Serengeti National Park....
If your 5-6 days includes time you want to spend in Zanzibar - it will be too rushed.