Persons have always assumed the origins of 5x5 are military in nature. That is indeed the case. On a communications scale over radio a perfect signal is rated a five, all degrees lesser being 4x5, 3x5 etc. until reaching zero which of course cannot be transmitted due to no reception is now available.
But where does the scale come from? In truth its also military and interesting in itself.
Before the advent of computers transmission of voice was simply done by radio, but transmission of "text" items was done by a teletypewriter device. In order for information not to have to be retyped every time is was sent to someone new, an automated TTY (Teletypewriter) was invented that could be fed a long string of paper approximately 1" wide and as long as the message needed. This paper "Tape" would be punched with holes in a vertical line that a "reader" recognize as a letter or number. The total number of holes that could be punched was Five (5). The holes locations and number of holes would constitute a specific letter or number.
Four holes (2 top 2 bottom center not punched) would convert the reader to numbers. Five holes would convert the reader to letters.
The clarity of transmission would affect the receivers ability to translate this message from its punched form back into regular text since static/distortion could change the hole counts making the message more difficult to read.
Four by Five or Five by Five meant near and perfect reception by the receiving TTY and the message was readable. Three by Five was understood but Re-transmission was probably expected, and Two by Five meant re-transmission was necessary.
So a readable Five punch TTY tape became the standard for military and civilian clarity in radio communications.
Hope you found this interesting.