My iPhone won't backup and is saying I have no iCloud storage when I should

My phone has been saying for a while, I have no iCloud storage and it hasn't backed up since May 2017. I'm switching my iPhone from an iPhone 5s to an iPhone 6. So I tried to sort out my iCloud storage. It turns out I was using a lot of storage on my photos, so I downloaded them onto my laptop. I kept around 100 of the very many 3000 photos! For a keepsake as I like having it there and now I'm using 542mb of storage for my camera roll. I now have 4.7gb available as I have used storage for other things. But on my iCloud storage it says I'm using up 4.06gb on my camera roll when I'm clearly not. And I want to get it to back up but I don't know how. I only have 5gb of iCloud storage and I'm not prepared to pay for extra, does anyone know what's going on and how I can solve it? My phone has been updated and it is on iOS 10.3.3

Did you try to delete pics directly in iCloud? ICloud seems to behave a bit strangely at times.

Anyway, I can tell you the best, safest and 100% foolproof way to back up whatever you want is macOS own Time Machine. Yes, you do need an external HDD but believe me it's worth it.

Ghgh

I would send all the pics to somewhere else like Google Photos which gives you unlimited storage for them (& videos as well).

As far as the rest, not sure. Of course only you have a detailed look at what else is there that could be holding up storage.

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