iPhone screen broken, iTunes won't let me do the backup because "not enough free space"

[nxpa76]

My iPhone 5s screen just broke up but the phone is still working, it's just that I can't see anything.
I tried to make a backup but then I got the "iPhone backup failed due to not enough free space" message, and I can't delete anything on the phone to get more free space because I can't see anything on the screen.
So, does anyone have any ideas or possible solutions to help me make a backup or to help me gain access in some other way to my phone's information?.

Thanks in advance!!!

(P.S. and I still have aprox 132 free GB on my computer, in case you think I don't have enough free space on my computer)

I've attached screenshots of the 2 messages I receive.

 

[C DM]

My iPhone 5s screen just broke up but the phone is still working, it's just that I can't see anything.
I tried to make a backup but then I got the "iPhone backup failed due to not enough free space" message, and I can't delete anything on the phone to get more free space because I can't see anything on the screen.
So, does anyone have any ideas or possible solutions to help me make a backup or to help me gain access in some other way to my phone's information?.

Thanks in advance!!!

(P.S. and I still have aprox 132 free GB on my computer, in case you think I don't have enough free space on my computer)

I've attached screenshots of the 2 messages I receive.

Sounds like you are trying to sync rather than backup.