How do I backup my iPhone to iCloud?

I've done it before on my old phone but now I want to do it on my 5s. I want to save my iMessages, photos, emails and notes. It shows memory on my iCloud has been taken up from my last phone, but I have 7 gigs more of photos that obviously aren't in the iCloud. I bought the extra 50 gigs. I don't have a computer or another phone. I keep trying to update my backup but it keeps saying could not be completed. People are saying I have to delete my old backup but I don't want to lose that stuff. How do I update it with all my new stuff? Also will there be a way to look at all those picture without having to put them on my new phone. Than

Hi there my name is Tyler and I can help you with backing up data to iCloud. Just wanted to let you know that I will share the way used on my ipad.

wich is mostlikly the same as your iPhone 5s as long as the software is up to date.
First of all go to the settings app on the home screen. When you get to settings go down to iCloud setting. Then go to your icloud/email then hit devices (2nd from the bottom) then chose your iPhone 5s then check last backup and see when the last backup was. If it was a long time ago then it will be time to update it. If it was recently updated then you can go to your iCloud account by going to iCloud.com and signing in. There you should be able to control your iCloud account.

If you need to update it the best thing to do is to use a computer but if you do not have one then you can go to the iCloud settings menu. Then storage and manage storage. After that go to iPhones backup. Then you can control it there. Hope I helped. Download Apple support app.