It is normal for an A4 sheet of paper to have grain running in the same direction as the long edge of the sheet. So common it can be relied on. The same is true of an A2 sheet ~ and an A0 sheet. I hope you can see a pattern here. It means that an A6 sheet is also long grain. The word normal is the troublemaker. For example buying A3 paper is ~ for most of the public ~ not normal. Similarly A3 paper is probably not normal. Time for a longer explanation ~
Machine made papers come out of the factory in huge rolls. As with all rolls of paper the grain runs along the length of the roll. If you cut or tear across a roll of brown paper you are working against the grain ~ you get a ragged edge ~ use scissors or a knife.
The huge roll of paper travels ~ by crane ~ it weighs tons ~ to a cutting or slitting room. This is set-up to produce the most common sizes of paper. To most folk that is A4.To the jobbing litho printer it is A2 ~ or SRA2. Some printing presses work better with a specific grain direction. The very lates print shops no longer use cut sheets and print straight from the roll ~ as do newspaper printers. The technical terms are sheet fed or roll fed.
The slitting and cutting machines reduce papers to A2 or A4 is demand requires. Demand for A3 is much less. Rather than cut to be long grain the general practice is to take a long grain A2 sheet ~ and halve it. Most A3 papers are therefore cross grain. This makes them ideal for folding into A4 folios for codex binding. Similarly an A5 sheet will ~ invariably ~ be cross grain. Which makes it ideal for folding down to make an A6 booklet.
My sub-head says unreliable. You may occasionally find non-normal papers. When assuming ~ or guessing ~ the grain direction ~ it can pay to stop and check.
If you are making A5 books then it is best that you find a supplier of A4 cross grain. It is not easy. We plan to make a variety of such papers available in our sister-shop.