While the registry of NC-05 was clearly seen only in "Home", according to Doug Drexler, it was the same shuttle that was seen in "Regeneration". [X]wbm No registry for the craft was established in the final draft script of either episode, nor that it was meant to be the same shuttlepod. The script of "Regeneration" describes the vessel as "a Starfleet shuttle," whereas the teleplay for "Home" characterizes the vehicle as "a Starfleet shuttlepod."
Doug Drexler didn't know why the NC prefix was chosen for the registry, other than the obvious reference to the Matt Jefferies plane. [X]wbm However, production illustrator John Eaves had previously assigned an NC-registry to the Sarajevo-type starship in a design.  The 05 registry number was a reference to travel pod 05 from Star Trek: The Motion Picture, a number frequently put on various small crafts throughout the franchise by the production staff. [X]wbm