Forgotten apple id password

In iPhone the password can only be changed , but cannot be saved and found in some locations and can be physically read and you can't bring back the same password particularly in iphone , if you had been using a Mac and signed in with same Apple ID and password in system preferences > iCloud , the password for Apple ID can be physically read if you had set up iCloud Keychain https://support.apple.com/en-in/HT204085

In Mac you had to open keychain access , tap the section of icloud , double click on Apple ID , click the box of show password , it will prompt to enter admin password see this article https://support.apple.com/https://support.apple.com/en-us/HT201487

But that is not your case , your iPhone is damaged , to reset password use a web browser , if you don't own it borrow from a friend or visit apple authorised service centre , open a new tab ( use command and T keys ) and see the steps in this article https://support.apple.com/en-us/HT201487

Note : the purpose of using a new tab is the friend or service centre guys must have with their own Apple ID and password in system preferences > iCloud , and to use your id they might hesitate to sign out their id and then permit your id to get signed in , this can be done but its a lengthy procedure , for that without signing out their id use a new tab .

For Problems With Your Apple ID

1. Forgot iCloud Password
2. Forgot Apple ID
3. iForgot Password - Apple ID
4. iForgot UserName - Apple ID
5. Apple ID Password Change
6. Apple ID Name Change
7. Apple ID - Apple Support
8. Manage your Apple ID primary, rescue, alternate, and notification email addresses
9. About your Apple ID email addresses
10. Get help with Apple ID
11. Contact Apple for help with Apple ID account security - Apple Support
12. What to do after you change your Apple ID email address or password - Apple Support

Reset Security Questions

Contact Apple for help with Apple ID account security

You may need to reach Apple’s Account Security department. If you cannot find your country or are not able to call, then complete this form and send it to them.

Try using Apple's iForgot service. If it says they don't have sufficient information, you need to contact Apple's Account Security team. To reach them, click here and pick a method; if you can't use any of the ones listed, fill out and submit this form.

it has been clearly explained about Apple ID password that it could only be reset , we are members in the forums and not as apple representatives , see this link https://support.apple.com/en-in/HT201232

And .

You can fill out and submit this form to contact Support, but it is unlikely they will give you your old password. One option is to delete the apps/purchases made by the other ID and download them using the new ID if desired. If necessary, check your purchases history to see which apps/purchases weren’t made by the current ID. 

Purchase History Review

Your old iPhone and its password are not saved in the device , as device is signed in with some web mail address configured with iCloud server account , the passwords are encrypted and can't be viewed , also this iPhone is damaged .

And after that you planned to sign in with same Apple ID and password in new iPhone 5s , but you can't do it for that you need a web browser and only can change the password but password can't be repeated and used one more time to sign in with new iPhone 5s ( unless and until you remember it ) , it depends that id was created with secondary authentication account ( in which three security questions and answers , rescue mail account is set and date of birth is added ) or you might had created a two factor authentication account .

If necessary, use the links Kappy posted to contact Apple Support.