Hi,
1) On your old phone, download and install Google Photos - complete the initial set up and allow the app to back up all your images / videos (may take a while)
2) On your new phone, download and install Google Photos - complete the initial sign in and your images and videos should be there from the old device
Failing that you could always connect the old phone to a laptop, move the images over to the laptop, then repeat the process for the new phone, only this time move them to the phone.
Side note - using Google Photos will automatically show your images / videos in Google Drive.