No, the subscription has nothing to do with your old serial numbers.
Okay, when I install CS5 Photoshop in another Computer, i want to use this Serial Number. This number is in my Adobe Account (https://www.adobe.com/de/account/my-products-services.html). But the Installation doesn't accept this number! Why?
More than one possibility:
• Perhaps you already have two activated installs on different computers. Maybe you forgot to deactivate one of those installs.
• Or, you may be typing the serial number wrong. This us especially possible if you don't have the original DVD case where the serial number is and you're trying to go by what you see on the splash screen or Info on your computer, and if that's the case, you're missing four digits, as Adobe truncates the numbers on purpose.
You are not addressing Adobe here in this user forum, and there's no one here who can check how many activations you have running. You need to Contact Adobe customer service directly, by phone or web chat.
If your CS5 serial is for an Upgrade you will need to enter two serial keys when you install cs5 on a new machine. The CS5 upgrade key and the key your product being upgraded. You previous upgrade or full product. Any cs4 or prior Photoshop version key.