The lens cone (not shade) is from a K-24. The K-24 shot 4.5" x 4.5" on 5" roll film.
Your camera is probably a home brew. Real aerial cameras are usually all metal.
By the time the K-24 was in use (WW-II) aerial cameras shot roll film. The sizes most commonly used by USAF were 5" (images 4.5" x 4.5") and 10" (images 9" x 9"). No 5x7. Did you measure correctly?
The 12"/5 Aerostigmat was designed sometime in the 1930s, is rated to cover 5" x 5" and isn't highly respected.