My screen cracked and I need to back up or transfer to new device, how can I do this?

[AC Question]

Screen cracked need to back up to transfer to new device

Dropped my S5, cracked the screen and the screen won't turn on. Getting a replacement device, so how do I backup my old S5 data to my computer to transfer it to the new S5 when I get it? I have tried the Google syn in the past from when I upgraded to the S5 from the S4, but some reason it didn't work and I lost a lot of my contacts.