Apple - Why doesn't my iPhone 5c support Night Shift?

From Apple site:

Night Shift is available on iPhone 5s or later, iPad Pro, iPad Air or later, iPad mini 2 or later, and iPod touch (6th generation).

So I think It's related to 64bit processor architecture.

You can install F.lux instead using xcode. It's not very complicated and it doesn't require you to jailbreak your phone at all and it's not a hack : https://justgetflux.com/sideload/ You'll just have to download the project file from another website as they've deleted it following apple's demand to take it down. It works nicely on my 5C.