Adobe Phtoshop download on new computer

Hi everyone, 

I bought Adobe Photoshop approximately 5 years ago now, and since I got a new Macbook last year I want to download Adobe Photoshop to my new computer. Obviously, I have the code from the edition I bought on my old computer, so I suppose I somehow can download that version down to my new laptop? I just don't know how to do it? 

It can't be true that I have to pay for the program one more time, can it? 

I hope some of you out there know what to do 🙂