Bought new computer and want to add 360 program, allowable from Home Computer product

I have Norton 360 on my home computer and it allows installation on up to 3 computers.  My daughter's laptop has one and I just bought another laptop and want to add the 360 program to it. 

 

I loaded 360 v.5 and it said I have 30 days before it expires.  I figure what I loaded was the pre-loaded program that came on the computer.  I looked for a product code (in the process I noticed I had Norton 360 v.4.3.0.5  on the home computer) but when I went to my account, it showed absolutely nothing on file under the Products and Order History pages.

 

Couple of questions:

 

How do I locate my product code? 

Will version 360 v5 be loaded on the new laptop or do I have to uninstall and reload 360 v.4, which is on my home computer?