Q: unable to delete mail account , using Iphone-5 , IOS 9.2

Hi vertex2512,

The information below provides a possible reason why your email account can't be accessed.  This applies to a POP account.    What type do you have?  What happens when you try to delete your mail account from your iPhone?  If you have a backup of your iPhone, you could restore it as New, and add only the Mail accounts that you want on the device manually.

Using a POP account with more than one device
https://support.apple.com/en-us/HT201855

About "Pop Locking"

The POP3 mail protocol was designed in some cases to support one connection at a time. When multiple devices attempt to access the mailbox at the same time, the devices may get locked out or you may be prompted to re-enter the account password.

Try to have only one device access the POP3 server at a time. If you are affected by this issue, wait 20 minutes before trying again, or contact your email service provider (ESP) to clear the lock.

How to erase your iOS device and then set it up as a new device
https://support.apple.com/en-us/HT204686

Back up your data

1. Check for iOS software updates. Install them if available.
2. Take a few minutes to transfer your content from your device to your computer to ensure that all of your critical data is safe.
3. Back up your device before you erase it.

Learn more about how to copy your backup to another folder, disk, or location for safekeeping.

Erase your device

Erasing all content and settings will delete all of the data from your device, including songs, videos, contacts, photos, calendar information, and anything else. All device settings are restored to their factory condition.

To remove all settings and information from your device, tap Settings > General > Reset > Erase All Content and Settings.

Add an email account on your iPhone, iPad, or iPod touch
https://support.apple.com/en-ca/HT201320

Take care,