A 7x5 matrix has 7 rows, five columns. Row Reduction constructs a stairstep pattern. If the columns are linearly independent, the RREF will show a diagonal of ones with zeroes above and below. Note that this is the "most common case," in the sense that if you generate a random matrix it's very unlikely this is what you'll get.
I can't seem to get the latex to work right now, but R will "almost certainly" have a 1 in the top left, and a diagonal of 1's, everything else 0. There will be two rows of zeroes at the bottom.
You need to consider other cases. Your answers should become clear.
You say you're not so clear on the theory? The best I can think of now is this: make sure you understand why the RREF has the same solution set as the original matrix. If that's clear, the rest should follow.