I purchased CS5 years ago, but attempts to download it now fail as my serial number comes back as invalid.

assuming you're using a valid adobe serial number (6 groups of 4 numbers), you have a mismatch between your installation file and serial number.  ie, you can have a valid serial number, but if it's for program A and your installation file is for program B, you will see an invalid serial number message.

common mismatches are language/region (eg, serial number is for western europe and installation file is eastern europe), platform (eg, serial number is for a mac and installation file is win), license type (eg, education vs enterprise vs individual).

and one of the most common is using a program installation file with a suite's serial number. eg, using a cs6 suite serial number with a photoshop cs6 installation file.  that won't work even though photoshop is included in that suite.  you must use the suite's installation file (and you can choose to only install one program from the suite).

here's official info about that error,  http://helpx.adobe.com/creative-suite/kb/error-serial-number-valid-product.html