What I do to cut an accurate square that I don't have an exact ruler for is this:
I use the closest, but larger ruler... so in the case of your 5 1/4 block I'd use my 6.5" ruler. Then I take two strips of narrow duct tape and mark off the 5 1/4" square by using the original corner of the ruler, but taping the other two sides at the 5 1/4" lines. So I have a 5 1/4" square inside my tape lines.
To cut, I cut the two sides that are the original corner of the ruler. Then I flip the ruler and line up my cuts with the taped sides, and cut the other two sides along the ruler.
Works great.