Why can’t my iPhone 13 hold much pictures?

You’ll likely need to rent more storage in iCloud.

5 GB isn’t nearly enough for a backup of all but a near-empty iPhone 13.

Here is how to manage iCloud storage: Manage your iCloud storage - Apple Support

And how to rent more storage: Upgrade to iCloud+ - Apple Support

evana258 Said:

"Why can’t my iPhone 13 hold much pictures?: I have 5GB, 200 pictures snd 17 videos. Why it says that it’s taking up 8.7 GB so I can’t turn iCloud back on…"

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Save a Few, and Export these.

So, export these, and then trash what is iCloud. You'd be just fine from there. Go here: Download Photos to your Mac from iCloud - Apple Support