In 5 days there will be a limit as to what you can see/do.
From Donegal, Sleave League cliffs have already been mentioned and must be top of the list. Afterwards drive to the end of the peninsula and visit Glencolmcille which has a lovely oldy worldy feel.
Spend a day pottering round the Donegal coastline from Dunglow to Dunfanaghy.
Travel to Derry stopping on the way to visit Glenveagh and the amazing Grianan of Aileach
http://www.maclochlainn.org/aileach.jpg
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From Derry follow the coastline past Downhill Estate and Mussenden Temple, Dunluce Castle, Giant's Causeway and Carrick a Rede rope bridge. Plan for an overnight around Ballycastle.
Next day take the A2 and head down the Antrim coast (for the Antrim Glens) to Belfast stopping at Cushendun, Cushendahl, Glenarrif Forest (waterfalls walk is really good), Carnlough, Glenarm...
If you follow tony2ohones suggestion, this route also works well the other way round. My only reservation would be that Portrush is too far for the first day as there is so much to stop and see on the way. You won't have chance to do full justice to the Antrim coast and glens.