Why Isn't My iPhone 5 with Apple Health Able to Record My Steps?

If you're wondering why your iPhone 5 or older models isn't recording your steps, it's because iPhone 5 and older models lack a ‘motion co-processor’/accelerometer, which is what is used to track your steps: see this Q&A from Apple for a bit more information.

Therefore you cannot track steps on your iPhone 5, or older models, directly using Apple Health. The motion co-processor wasn't included inside of iPhones until the iPhone 5s series and beyond. According to Apple's site, you will need to use another app to record your step data, and then import that data into Apple Health. You might want to contact Apple support if you have any other questions about which app(s) would be best to pair with Apple Health for iPhone 5: https://getsupport.apple.com/