Photoshop still on trial version after instalation

We currently don't sell versions of CS prior to CS. If you just purchased CS5,I am guessing it was from another user. Did you transfer the license?

If you sell or give your Adobe software to an individual or business, you can transfer the license accordingly.

Adobe licenses need to be transferred when they change users. Transferring the license allows the new owner to register the software in their name. Both the transferor of the license and the recipient must complete a Transfer of License form. The product serial number must be registered in the Adobe profile of the transferor to transfer the license. You must qualify under the Transfer of License policy.

Transfer an Adobe product license

Adobe Transfer of License form

If you  purchased the software and are the first to license it, please see this document:

Activate and deactivate Adobe products