Installing iOS 11 on iPhone 5c?

Solution 1:

It’s not possible. The iPhone 5c has a 32-bit CPU, and iOS 11 has dropped 32-bit support and will only run on 64-bit CPUs. Apple will let you install it on any phone that can run it at all, which is the iPhone 5s or newer.

Solution 2:

No, this is not possible.

I don't want to have to buy a new phone if this one will still work...

Your iPhone will still work with its current operating system, though. Don't feel you need to upgrade, only get a new phone if you really want to.

As to "why", there are many reasons. For one, as Mike Scott mentioned, the iPhone 5c has a 32-bit processor, and iOS 11 requires a 64-bit processor to run. Secondly, the operating system has various aspects which rely on the exact device you own. Depending on whether you have an iPhone or iPad, a GSM or CDMA phone, and so on, you need to have a slightly different version of the operating system. In order to run on a certain device, Apple needs to develop a version of it specifically for that device.