The nicest parts of the island are the south/southwest, the west, and the northwest
So basically between one end of the Wild Atlantic Way (Derry) & the other (Cork) and a lot of the inland bits adjacent
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You're not going to get it all done in 5 days so choose a 'corner'. As Hatcho says probably head straight to Galway. There's some nice roads away from the motorway but you probably won't have time if you're going for the good bits. Once in / near Galway either go north or south.
The road north will bring you into Connemara, my favourite part of the country, and subsequently Mayo where you could certainly spend a couple of days exploring the mountains, lakes & shore. Achill Island is a day trip all on it's own & Belmullet peninsula too although there's less options of roads. If you still have time carry on north through Sligo & Donegal with the Sperrin mountains & valleys not too far off your route. Malin Head north of Derry is the northern cardinal point
Turning south in Galway will bring you through Clare, with it's stunning karst landscape around the Burren, into Kerry & west Cork with their mountains (the highest one in Ireland is down there), lakes & coastline. There's any amount of roads, and several stunning passes (Conor Pass, Healy Pass, Ballaghbeema Gap, to name just a few) in this corner to keep you occupied for the duration of your trip & keep you coming back for more. Slea Head, our western cardinal point is in Kerry and Mizen Head, our southern cardinal point is in west Cork. Mizen Head has a visitor centre & a small cafe.
If there's only you, or you & her, you shouldn't need to pre-book accommodation. It won't be anywhere as busy as July & August and you'll be more flexible depending on how your days go. B&Bs have gotten ridiculously expensive & often rival hotels price wise but overall the standard is very good these days so you don't really need recommendations which will only end up putting you under pressure to get there for the night. Have a look at booking.com over lunch & decide how much further you want to go that day & pick appropriate accommodation. Even if it's not the Ritz you're only there for one night...
A word on Irish 'roads'. The motorways (M), thanks EU, are modern & generally flow well. Speed limit is 120kph. But jaysus they're boring on a motorcycle. Our N (national) roads are either 80 or 100kph. Quality is generally dependant on where they go to & from - main arteries are generally better maintained than less busy roads. Regional (R)(usually 80kph) roads are generally smaller & more rural so the surface may not be as good. And then we have local (L) roads. The speed limit on most of these was recently reduced to 60kph & the change is obviously making money for the government as there's camera vans regularly parked at the side of them. The surface on these varies from 'ok' to almost green lane standard. Some won't even appear on your GPS. On R & L roads an average speed of 50kph is good going, 60kph is virtually impossible to achieve without putting yourself in harm's way. The standard of driving here has deteriorated hugely over the last decade or two so take care
Any questions

GPX routes are available, PM me with your preferences
PS: Although most of the photos are gone & some of the links are broken there's lots of Ireland info here -
Hopefully this will turn out to be a guide to travel and things to see in Ireland.
Any of you with some useful information about and things to see and do and places to stay and the best roads while in Ireland place your posts here.
Try to keep the posts informative with as much detail as possible with pictures if you have them....i will try and edit the posts in the best way possible to keep the info neat and tidy
I'll start with a couple of links that covers Ireland with general information.
Nice pdf map file of NI with places of interest and some info
here is a fast and...