My iPhone 5 won't power on and I'm trying to recover my pictures/videos?

I never used iCloud. I tried going through iTunes however, I have a passcode on my phone (and can't power it on to see the screen) so I can't recover it that way. When I plug it into the charger, it keeps vibrating like it's charging every 10 seconds. So it's dead. Is there anything I can do to recover my pictures and videos? I appreciate any help you can provide. Thanks!

Added (1). and I haven't made a back up even before it was broken

Once you get your new iPhone they can transfer your pictures and everything onto the new phone. When I went from my iPhone 4S to an iPhone 6 I got everything that was on my iPhone 4S including pictures, videos, even all of my text conversations transferred over. I don't think you need to go anywhere to do it either. If you had plugged in your phone into your laptop and let it back up your phone, then when you plug in the new iPhone it will ask if you want to set it up from previous iPhones, just select the iPhone that is broken and it will transfer everything for you.

If won't power on try charging phone a few then hold Power and Home buttons down together till apple logo appears n let go both buttons