how to remove an apple id on the iphone 5c?

You need the Apple ID and password that was used when the device was first set up. If you don’t know that, you can’t remove the Activation Lock.

If this is a used device, the previous owner needs to go to https://www.icloud.com/find/ and erase the device, then remove it from their account. If they won't do that, the device is useless. Apple won't unlock it.

Turn off Activation Lock - Apple Support.   *

If you are the original owner, contact Apple. Apple can remove the ID  if provided the required paperwork to include the original purchase receipt with the serial number on it. 

Request additional support for unlocking your device.    -

You used to be able to take the device, the original purchase receipt with the serial number, and a photo ID to the nearest Apple Store (if it has reopened) and have them remove the ID. This may have changed, so call the store before going to make sure they can help.

Genius Bar Reservation and Apple Support Options - Apple.   -

Read carefully, see -> How to delete your Apple ID account

How to delete your Apple ID account – Apple Support (UK)

See -> How to deactivate your Apple ID account

How to deactivate your Apple ID account – Apple Support (UK)

Scroll to ->  How to temporarily deactivate your Apple ID

Sign in to your Apple ID account page on a Mac, PC, iPhone, or iPad. Then scroll down to Data and Privacy, and select "Manage your Data and Privacy." On the following page, select "Get started" under "Deactivate your account." If you don’t see this option, it means that this feature is not available in your country or region. 

👉 When you request to deactivate your account, you receive a unique alphanumeric access code. Make sure that you keep this access code in a safe place—you must have it to reactivate your account. 

FYI: you can't merge multiple Apple ID accounts.

See also this Apple article: Change your Apple ID

Change your Apple ID - Apple Support (SG)