If both laptops are purchased with Windows licenses, there will be no problem at all. Windows will detect the new hardware, read and activate its license without bothering you.
I have a Dell Inspiron 15-3567 with an i3 and a 1TB Toshiba ATA hard drive. Is it possible to simply swap the hard drive out to a Dell Inspiron 15-5567? I looked and the specs and they look the same but I don't know if the drivers are compatible. It looks like they have the same type of Toshiba HDD drive.  
Dell 15-3567 i3 compatibility with 15-5567 i5