The serial number should be on the DVD case.
If not, did you register CS5 with Adobe? If so, you can log in to your Adobe account and retrieve it there.
If not, try running the Belarc Advisor http://www.belarc.com/free_download.html
Re: upgrading - the current version is CS6.
You can download the free trial version of CS6 from the Adobe website and try it out for 30 days to see if you like it. If not, you can uninstall it and continue using CS5.
I ordered my product from Journey Ed web site. student edition I thought I registered it with Adobe but cannot find itthe link for passwords. I found the orders history but since I don't purchase it from the Adobe site well of course it wouldn't be there.
If you actually registered it with Adobe, it might be listed in the My Products section, which is nearby but not the same as My Orders. It's worth a look.
If you truly have lost your serial number utterly and completely, you may be out of luck, though I would certainly try calling Adobe customer support and appealing to them humbly.
It's really no different than losing a $100 bill. Possession and protection of information can be just as important as with physical things. Most folks make media backups of things they purchase and write the serial number et. al. down on the media or on the case.