restore replacement iphone 5 from damaged iphone 5
Apple has created help for such situation.

If you forgot the Apple ID use the https://iforgot.apple.com/appleid



If you forgot the password or the Apple ID use the 
Answer your security questions


Use these steps if you know the answers to your security questions:

Select “Answer security questions,” then click Next.
Select your birth date, then click Next.
Answer your security questions.
Set a new password and select Reset Password.

Manage your Apple ID primary, rescue, alternate, and notification email addresses


Add, change, or delete the several types of email addresses you can use with your Apple ID account. Primary email address

Every Apple ID account has one primary email address, and that address is your Apple ID. When you create an Apple ID, you enter the primary address to use as your Apple ID.


Your primary address is also the contact email address for your account. Check it regularly, because it receives email that you need to manage your account. For example, before you can use a new or changed Apple ID, you need to verify it as directed in a verification email that Apple sends to that address. Didn't receive the email?