Your problem is not connecting 2 different categories of cable the certification of the cable make that possible.
Your problem is you have at least 1 fake ethernet cable. All flat cables immediately fail the requirement on wire size. In addition CAT7 cables require very special orientations and shielding that also make the cable a lot thicker and stiffer. Not that it really matters you likely do not need better cables than cat5e since it supports gigabit speeds to 100 meters.
So maybe it will work and maybe it won't fake cables have all kinds of issues especially when they are longer.