Is there any way to recover the contacts from this phone?

Hi, a friend of mine brought his iPhone 5 to me after his display stopped working. I figured a new screen would sort the problem. After putting a known and tested working screen on the device, it still shows no display.

The phone is otherwise working fine except that there is no display and digitizers are unresponsive on the device (it still buzzes and beeps, and is recognized by the computer). I've told him that he basically needs a new phone as the damage is on the boards side. However, he desperately needs to save the pictures and contacts on the phone.

There is no iCloud on the device but there is a passcode, and without being able to type in the passcode or click "Trust", we can't link it to iTunes. There is also no other computer that the phone has synced with that will automatically pass the "Trust" window.

Is there any way we can possibly get data off this device?