How to recover photos from my Iphone 5?

Ok, I got my iphone about a month ago, and dropped it today at school. The screen has got white strips running down it, and i can't use the touchscreen. It was insured, which mean i'm being sent a new iphone on wednesday, but i need to take the sim card out of my old phone, and send it to apple care with the charger. They told me to sync it to keep my stuff.problem. When i try to sync, it tells me to enter passcode. I can't use the touchscreen to enter my passcode. I have tried going into recovery mode but realised that will lose all of my photos. Is there anything i can do to get my photos? And is there anyway to bypass the passcode? Btw, i haven't yet synced the iphone due to problems with my laptop. I need these photos. There are photos of my late grandfather on them.

Added (1). What jade?

Added (2). Screen is absolutely fine, the only problem is that the screen won't respond. By absolutely fine i mean no cracks or anything, there are white strips and tears on the screen, and it is non responsive

Ok this is what you do…

Heres a suggestion.go on like google images and look up a picture of a iphone 5 lockscreen and take yours, put it beside the picture and try your best to punch in the code without seeing the actual screen, if the touch screen is still responcive that is