Why is it that my iPhone 5 is too full for me to take a photo, but my iCloud has 17 gigs of space available?

Good Morning akakk,

When you take a picture on your iPhone, the file is saved to your internal storage on your iPhone, and a separate copy is saved to your Photo Stream if you have that feature turned on in iCloud.

The resources below will explain how to manage the storage space on your iPhone and free up space if you need it.

See how much storage you've used on your iPhone, iPad, and iPod touch - Apple Support
https://support.apple.com/en-us/HT201656

I take a lot of photos and videos on my iPhone, so periodically I need to transfer them to my computer to back them up to a local hard drive and free up space. Here's how:

Import photos and videos from your iPhone, iPad, or iPod touch to your Mac or Windows PC - Apple Support
https://support.apple.com/en-us/ht201302

Cheers,

- Judy