Good morning Martina,
Thanks for clarifying! :) It's wonderful that you have five whole weeks to travel around, and if you have the time you should definitely include the Causeway Coast into your itinerary. You can find some ideas here
The Causeway Coastal Route has signs which say 'Scenic Route' and these are generally not accessible by larger vehicles. A lot of the small roads along the Northern Irish coast will have signs which mention these restrictions as well, but you'll still be able to reach most of the highlights, like the Giant's Causeway, without any issues.
Take a look here for more information about the Gobbins
. The visitor centre is easily accessible, and from there on you hop on a bus to the cliff path with your tour guide.
In general, the roads on the island that are closer to the coast can be more steep and narrow, but the main roads that Cindy mentioned in her earlier reply should be fine. :) For the areas that aren't accessible, you could always choose to go on a guided tour so you won't miss out on any of the sights.
I usually find that Google maps gives you a good idea of what the road looks like and this way you can judge if you'd be comfortable driving there. If you'd like to look into the accessibility of any of the individual routes and sightseeing spots, I'm always here to help!