Your examples are using Descriptive notation. For example, "Queen to Rook 5" (Q-R5) means "move the queen to the fifth row of the board (viewed from my perspective), and to the same column that had a rook in the starting position". You may notice that "Rook 5" could refer to two different squares, one on the leftmost column of the board and one on the rightmost. If you needed to distinguish between the two because the queen could move to either square, you'd say something like "Queen to King's Rook 5" (Q-KR5).
Descriptive notation was popular in English-speaking countries for most of the 20th century, and if you buy a chess book written before 1980 the moves will likely be in this format, but it is now basically obsolete.
Everyone has now pretty much moved over to Algebraic notation, which is much simpler. The rows of the chessboard are numbered from 1 to 8 moving away from White, and the columns are lettered from a to h from left to right from White's point of view. So White's move "Queen to King's Rook 5" in descriptive would be "Queen h5" (Qh5) in algebraic, and Black's move "Queen to King's Rook 5" would be "Queen h4" (Qh4).
Algebraic notation is much simpler than descriptive and is also the overwhelmingly more popular method of describing chess moves today, so I recommend that you use it.
My query for "king to rook 3" didn't bring anything useful in google, so thank you for directing me the right place, SReynolds, even though I don't know why I shouldn't consult here, where I know I will get the best relevant answer, just like anybody else. But thank you for your help, once again.
I wasn't trying to imply that you shouldn't have asked, it's just that a very simple Google search could have come up with this answer a lot faster. My first 3 Google results when searching for king to rook 5 are pages explaining this notation, but my Google is set to English, so that might be the reason.