Adam has an old 2007 iMac that still runs well, but it's not very good for the Internet. He wants to use it as a secondary computer next to his newer iMac. Leo says to make sure both computers are attached to the same iCloud account. That will make sure that the older Mac is synced properly. Leo also said that it's likely running iPhotos, the older version of Apple Photos. So it may have iCloud turned off. So turn that on.
Leo also says that it's a good idea to manually move the iPhotos file to an external drive to back it up. R/C the iPhotos Library - select Show contents - original photos. Take those photos and copy them over to an external drive. Then connect it to your new iMac and import them into Photos. From ScooterX - here's how. You may lose metadata if you edit them though. So start with the originals when you back them up.