That doesn't mean that bluegrass style is completely useless for British music. Ray Chandler is one English banjoist who has successfully adopted what is basically bluegrass banjo style into something that is genuinely British.

Fiddle style

But since you're here, you're probably not interested in how to get an Irish tune to sound like bluegrass, but rather how to get a five string banjo to sound "Irish."

The "fiddle style" usually associated with "authentic" Irisg solo banjo is a bit trickier on the five-stringed banjo. It can be done, but it takes some effort and there'll always be some limitations.

The three most important points are:

Forget all you know about banjo technique
Ireland and USA may be just an ocean apart physically, but when it comes to banjo playing technique, they are separated by several universes. If you have some mandolin or guitar flatpicking experience, you're much better off using that as the basis for your "Irish" banjo style.
Get a flatpick.
There's no way to get the Irish sound or those fast triplets by fingerpicking.
Play only the tune.
No chord notes or anything like that - well not many of them at least.
Do whatever you want with the fifth string as long as you don't touch it while you're playing!
Generally there is very little useful you can do witht he fifth string: you don't want that high g or a ringing all the time, and nine times out of ten it's technically easier to do without.

If you want to go a step further:

Use the "Irish tenor banjo" right hand position witht the little finger anchored on the banjo head close to the bridge.
Tune the first string up to an e.
The "Chicago" or "Guitar" tuning - DGBE seems to be much better suited for Irish solo playing than standard five-string banjo tuning DGBD / DF#AD (remember we leave the fifth string out). The tunes often reach up to a high a, and it's a great advantage to be able to reach that note without changing left hand position.

Other styles

The problem with playing traditional Irish banjo style on a five-stringed banjo is that you are working against the chracteristics of the instrument. The style is really tailor-made for the tenor banjo, and if you are going to play it a lot, you really ought to get yourself a tenor.

There are other "authentic" Celtic styles though. Playing guitar style on a five-string banjo may not be such a good idea since it tends to end up sounding like bluegrass, but both harp style and dulcimer style are good alternatives, well suited for the five-stringer.

Accompaniment

The tenor may be the solo banjo for Irish music, but when it comes to rhythm playing, it's the five-string banjo that is the most common one.

The most important Irish rhythm banjoists of recent years are Luke Kelly (from the original Dubliners crew) and Tommy Makem (from Clancy Brothers. Both played five-stringed banjos but had very different styles; Luke Kelly belonged firmly to the European minstrel tradition, modelling his style after Margaret Barry, while Makem learned the banjo in the USA from Pete Seeger's books and stayed with Seeger style folk banjo.