You should find your serial number under the Adobe ID you used when you registered CS5 with Adobe.
https://www.adobe.com/account/my-products-services.html#MyProductsHeader
If it's not there, Contact Customer Care by phone or chat. Hopefully you have proof of purchase.
Adobe customer support is your best bet for getting a new serial number. Be sure to present them with as much proof of purchase as possible when you contact them.
Gene