Any "generic" 5300 should work in dells. A lot of generic cards sold happen to be dell parts anyways, with a separate dell p/n as well.
The HP/Lenono parts are not interchangeable in my experience: Those cards require the branded laptop bios and its a two way street, the laptop bios requires the hardware id to be in its whitelist.
Its usually not a concern, the truly generic parts seem to be cheaper and more available with only a few exceptions.