The Bank of Ireland token could certainly be considered "currency". 1805 was in the middle of the Napoleonic wars, and Britain was running short of official coinage. To help fill the gap, the banks (Bank of England and Bank of Ireland) issued their own tokens, with designs and even denominations distinctive from official crown coinage, so nobody would get confused. These tokens are listed under "Ireland" in the world coin catalogue, under "token coinage". The 5 pence of 1805 is worth (in the American catalogue) US$7.50 in Fine, $25 in Very Fine.
As for the other one, it would be a modern, private token issued by the company listed on the front. Not much can be said about it's origin or date of issue, except with "5 shillings" it must predate decimal currency. It would not have seen widespread circulation or general acceptance as money. Such pieces are only listed in specialist catalogues, assuming that Irish numismatists have been interested enough in these pieces to study and catalogue them in detail.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis