How to update the iOS on an iPhone 5c?

The iPhone 5C can be updated to iOS 10.3.3. To accomplish this, see: Update your iPhone, iPad, or iPod touch - Apple Support

And: If your iPhone, iPad, or iPod touch won't update - Apple Support

If the above Apple articles do not help, please post back with relevant information. 

Chances are, you already have the most recent update for the iPhone 5.

Frankly, you are going to need a new phone if you want to run newer apps that require iOS 15 and iOS 16.