Q: apple ID change not updating on iphone 5c

Actually you need to log out of

Settings - iCloud - Find iPhone and then

Settings - iCloud - Log Out

Then you will be able to sign in with the new ID

You need to sign out of your old Apple ID using the previous password.

Note if you have instead created a new Apple ID, you cannot update all your apps with the new Apple ID & password. 

It is getting it from iCloud and Find iPhone

The other thing you may be able to do is to log into https://www.icloud.com

Locate the device and erase it from there

Read here: Change your Apple ID - Apple Support