I know the phrase "put two and two together", and in fact someone has already asked a question regarding its origin. However, I recently heard someone say the phrase with an addition of the humorous "and got five". Is this part of the original saying? If not, was it coined and by who?
"Put two and two together and getting four" is from at least since 1816, see my answer on this similar Q&A.
"Put two and two together and getting five" is from at least 1859.
From The New England farmer: Volume 11, in 1859:
The classes had nearly been through with their morning lesson, the older boys and girls had taken slate and pencil, and were trying to put two and two together so as to make five, and all as bust as they well could be when tap, tap, tap, whir-r-r-r-r-r-r, went somebody or something on the outside of the school-house.
Albany de Grenier Fonblanque in c.1860, in Hector Mainwaring; or, A lease for lives
Prudence, as well as inclinination, urged the match ; for two and two put together carefullv, will sometimes make five. Marion's little fortune would serve at capital to push Clement on in his profession--he promired soon to be famous in it--the gallant, clever lad - and repay her fiftyfold.
The Hon. Mr. Dorion in 1865, in the Parliamentary debates on the subject of the confederation of the British North American Provinces
It is said that this Confederation is necessary for the purpose of providing a better mode of defence for this country. There may be people who think that by adding two and two together you make five. I am not of that opinion.
Here's Frances Eleanor Trollope in the The Fortnightly Review from 1870, in the serialisation of her story Anne Furness:
"He's a cunning man, and knows how to put two and two together and make five of 'em 'stead o' four."
So it looks like getting five came a bit later than getting four, and possibly from Canada/north America.
Edit: to include earlier references.
Edit2: Or to look at it another way, "Two and two is four" is from at least 1655 with plenty of 17th century references.
"Two and two make five" is from at least 1690 with plenty of 18th century references.
Nay, the points of any other inward line parallel to this, will do as well as the points of this middle line, which is as plainly true, as two and two is four, if thou understandest sense when it is propounded to thee.
This is as true, Tom Vaughn, as two and two are foure, though I do not call you Owl for your ignoreance, as you do me for my knowledge.
For as one can never make a Man believe that a Square hath but three Corners, and that Two and Two make Five ; so one can never make him believe that Ingratitude is an Ornament to the Nature of Man, that Injustice merits a Reward, ...
Wikipedia gives "two plus two equals five" as a slogan from George Orwell's 1984, with the suggestion that if everybody believes something to be true, then for all practical purposes it is true (i.e consensus reality).
For me "putting two and two together to get five" is about combining different pieces of information and then drawing unjustified additional conclusions.