Should a new concrete porch, 5' x 7', have a saw cut in the middle of the porch? I've never seen this before.

"A saw cut"?

Do you mean a control joint? A line cut?

5 x 7 is usually small enough that it isn't required, but they may be a reason for it. How think the slab is and what will be loaded on it. Can't be certain without seeing the site.

If you will be covering that cement floor, I would not worry much about it.