You'll need 130 GB of space, maybe a bit more, to copy the files in the manner you describe. Steam first checks to see if you have enough free space to install the game, then it checks to see what files have already been copied to the machine. So you'll need 65 GB of space to store the copied files and additional 65GB of free space just so Steam won't refuse to "download" and install the game.
Probably the easiest way to work around this problem to use Steam's own backup and restore functionality to copy the game between computers. You'll need 65GB of free space on your home computer, and 65GB of space somewhere else. If you happen have a big enough portable USB drive, either a portable hard drive or USB key, than that would be ideal. Otherwise you can use a folder on your main computer and share it over the network. To perform the backup right-click on the game in your library and select "Backup Game Files...". To do the restore select "Backup and Restore Games..." from the "Steam" menu at the top left of client. Make sure to delete the Grand Theft Auto V files you've already copied to the home computer first.
(I've more detail of the backup and restore process in another answer.)
If you have 130 GB of space free on different hard drive on your home computer you can also create a secondary Steam library folder there, copy the GTA V files to secondary library and then "install" the game to that folder.
