I'm thinking that the finished block (using 9 five-inch squares to begin with) would end up being only 13 inches.
With the first sewing - the original 9-patch - the block will measure 14 inches (unfinished)
With the second sewing - reassembling the cut up pieces - the block will measure 13.5 inches (unfinished)
There will be 1/4 inch "lost" on each side when the blocks are assembled - so the blocks will finish to 13 inches
If my math is right.