If I want to free up storage on my iPhone 5?

Note: I'm technologically challenged btw. My husband is the one who knows all the newest techno terms and how it all works, not me. So please forgive me now for any confusion caused by my ignorance.
I have an iPhone 5 and it came with 16GB of storage on the device. My iCloud came with 5GB free space and it's not even full yet. I have 2.3 GB space avail in iCloud. I only have my iPhone & iPad linked to my account. Less devices less data stored? BUT! My phone won't let me take anymore video or photos. It just says "manage storage" So now realizing that I finally understand the difference between my devices storage and my iCloud, is it a bad idea to just delete all my photos from the camera roll on my iPhone? They should be stored in my iCloud as I have it set in my backup's to do so, right? My photos take up a huge amount of space on my phone. However these are pics of my children, family, birthdays, everything! I would die if I lost them by stupidly erasing them from the device just to "manage storage" I want to know what you think? Good idea? Or bad?
I can always back up on my PC but I need my husband to do this for me bc I'm completely inept. And he always puts my requests off for a long time and I can't wait anymore. I need my storage space freed up so I can take pics and download newest version of iOS.

http://support.apple.com/.../kb/HT4083

Google is also sometimes a wonderful place to start searching for how to use a computer better since it's an invaluable skill to have in the modern world. Once you back up your photos to your computer by following the steps in the above link, then you can start erasing photos from your phone.