How can I record my iPhone 5C screen

The article you attached above explains that iOS 11 is required to do screen recordings.

The maximum version of iOS for the iPhone 5C is iOS 10.3.3.

Therefore, your screen cannot be recorded. You would need to purchase a newer iPhone to record the screen.

The iPhone 5c can only update to iOS 10.3.3 max.

To record the screen you will need iOS 11.x which you can do using iPhone 5s or later models.