Use iCloud storage space to free space from iPhone 5s
It will depend on the root cause of your storage being full, so start by checking on Settings &gt; General &gt; Usage, and select Manage Storage from there to have a detailed view.



In my case, pictures are using a lot of space, and podcasts are just behind.

If you click on any of the items on the lists, you get more granular options



Here I clicked Music and I'm able to see which albums are using space.

If I slide "All music" to the left I and click Delete I can remove it from my iPhone from here, and recover 1,9 GB of space; of course you have to be cautious and be sure you have that music somewhere else (on your computer, on iTunes Match, or if you purchased it from iTunes Store, you can re download it when you need it).



If it is full of pictures and videos, you can activate iCloud Photo Library and store full versions on iCloud, keeping low resolution copies on your device; that will free up some space.
If it is music, iTunes Match or another streaming service will allow you to delete music and download —or stream— on demand.

Other than that, check Whatsapp and iMessage which are huge space eaters —because of images and videos sent and received with those services; you can delete those images and videos if you have copies of what is worth saving.

iCloud will be very useful for backups and synchronized documents between your Apple devices, but your question indicates you hoped to somehow move some of your data from your device to the cloud, which is called selective syncing on other services (Google Drive, Dropbox); I couldn't find info on that —or similar— feature in iCloud, and I believe it's not possible.