Hello. Welcome to Android Central.
Not old, probably still the most prolific phone on these forums and a premium device.
You can go to My Files (icon in the Samsung folder) and select the photos to move to external sd card.
Personally I would drag them to a pc with usb and move them to the new phone.
You also have cloud storage like Google Drive or Dropbox.
Contacts is easy as your Google account should bring them to your new phone if you use the same account.
Look in General - Accounts - Google touch name, check that contacts are synced and turn master sync on.
Also use your Samsung account to sync. Samsung Kies on a pc is another way to copy media like photos and music.
With Contacts, I think only Google merged contacts will copy, you may have some on the Device only.
You can check your contacts now on your Gmail inbox page on a pc (many don't use a pc) or browser.
Enjoy your new phone. Larger screen?
Sent from my SM-N9005 using Tapatalk Pro