Will I be able to recover my photos (not downloaded to computer) after performing a restore on my iPhone 5? I overloaded my capacity and the screen went blank and it will not start up.

I did not have the latest version software on my iPhone 5- probably the version it came with. I have been going to the limit of my storage capacity and yesterday my screen briefly showed what looked like a multicolor UPC code or old-fashioned TV "dead air time" image and then just the apple symbol for a very long time. I tried restarting the phone and ended up pushing every combination of buttons until the phone went dead and I haven't been able to power it on since. I am reluctant to do a restore, as I will lose many photos that were not yet downloaded onto my computer (and who knows what else?). Is there any way to ensure that I won't lose my photos is I restore the iPhone?

Thanks very much for any help.