Yesterday I purchased GTA V for the PC via Steam and downloaded it onto my laptop at work. When I got home to transfer the 65 GB worth of files to my main computer, I cleared up 65 GB of space on my SSD and have just enough room to fit those downloaded files onto a Steam folder that I created. However, Steam won't recognize the game as installed. I tried to click the "Install" button for the game where it's currently pointed to the folder where I've copied all of this data, but after exiting Steam and opening it again, it's saying that there isn't enough room to install the game. I spent several hours looking up ways to solve this, but I haven't been able to so far.
Also, Is 65 GB enough space for this game, or will I need to clear up more room for it?
Edit: After following Ross's guide below, everything worked fine with the backup process!