Did you not write your downloaded install file(s) to a backup DVD or copy to a USB hard drive?
If you no longer have your downloaded install file(s) you will need to download them again
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Do I first reinstall CS5 use the serial code then download CS6 upgrade and then use that serial?
Welcome to Adobe Forum.
Please download & install the CS6 version, you can the product download from
While installing , it will ask you to insert the CS6 serial number, after that it will ask you to insert the previous version qualifying serial number, at this time you need to enter the CS5 serial number & it will be installed & activated.
You do not need to install the CS5 on the new computer, you can directly install CS6.
Please let us know if it worked.