I can not activate my iPhone 5C purchased second hand

What you are encountering is Find My iPhone Activation Lock, a security feature in part to deter re-selling of stolen devices.

Turn off Find My iPhone Activation Lock (formerly: Activation Lock: Removing a device from a previous owner’s account) - An activation lock can only be removed using the log-in information for the account that applied the lock.

https://support.apple.com/HT201441

Get the owner of the account to remove the lock or return the device for a refund. The device is otherwise useless to you.

If the owner has not provided contact information as a message showing in the login screen, there is no way to contact the owner unless the person who gave you the device knows them.

You are still out of luck then. Only that person can disable activation lock for you. If they can recover their AppleID (If you forgot your Apple ID - Apple Support) then they can release it from a web browser - Turn off Find My iPhone Activation Lock - Apple Support

If your office is the original owner, have a company designated representative take the device, the original purchase receipt with the serial number, and a photo ID to the nearest Apple Store.

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or contact Apple ID Support. They will need to see the original purchase receipt/paperwork also.

Apple ID Support

Apple ID Support (2) 

Apple Support by e-mail or chat         Select your device, Battery, Power and Charging, then Power adapter not working to get a chat option. 

Apple Support using Twitter

Or fill out and submit this form.

I am afraid so, if the seller cannot help you or is unreachable. Activation lock is an anti-theft measure and is enabled and disabled by owners. It’s quite possible the person who sold it to you sold you a stolen device.

Nobody here nor at Apple can help you. Contact the seller and ask them. But without the AppleID and password used with activation lock, you can do nothing to setup and use that device yourself.