Camera refuses because 'SD-card is full'

But the SD-card has 5GB left and pictures are stored in telephone memory anyway.

Which software is running on your FP3?
Did you format the SD card as internal or mobile storage?

I had this issue once, when a music streaming app filled my storage with cached data. Any other app was able to claim this cached storage, except the official camera app.
This is a bit tedious to check, since cached data is not shown in the data statistic in the settings app, but you need to check each app one by one.
After i cleared the cache of the music streaming app the default camera app is working again.

Thanks for the reply. Somehow it works again.