How can I transfer Photos from an old iMac to new iMac?

·       Always connect your old Mac's Time Machine External Hard Disk prior to startup, this will allow a migration from your TM backup and it will be dead simple! When you start the new Mac for the first time it will startup Setup Assistant (SA), SA will get to a point where it asks if you are migrating from another computer, select Yes and follow the on-screen prompts and it's done! It is that simple! This is the easiest, quickest and most reliable method to migrate from the old Mac to the new Mac is to simply connect the old Mac's Time Machine External Hard Disk to the new Mac using a USB cable before you turn on the new Mac. 

·       NOTE 1: You will likely need a USB A to USB C adapter, you can find them on Amazon for $10 or less. Something like: 

·       NOTE 2: If you have already done SA on the new computer then simply connect the Time Machine External Hard Disk using a USB cable and launch Migration Assistant (MA) which is located in Applications - Utilities - MA. Then follow the on-screen prompts.

·       The ONLY difference between MA and SA is MA will create a new user account that you need to log into.

Both SA and MA migrate applications (not 32 bit apps), data files & settings. They do not migrate Mac OS itself. Some professional apps such as Adobe and Microsoft apps may require re-installing their apps as they will not allow them to be migrated. As long as you kept the security keys for installing their apps, it is not an issue. 

Finally, my recommendation is not using Wi-Fi when doing Setup Assistant or Migration Assistant. Why, it simply fails in a lot of the cases reported in these forums. A wired connection is more reliable and the last thing you need is a failed migration when there are safe methods readily available. Please read and follow the directions in Setup Assistant and Migration Assistant. If you do not have a Time Machine backup of the older Mac then create one!If you are not aware of Time Machine, please read Back up your Mac with Time Machine and finally if you need an External Hard Disk to use as a Time Machine External Hard Disk then many experience users on these forums prefer the OWC Mercury Elite Pro due to it's reasonable price, high level of quality and ease of use. 

This is the smartest and quickest method. However, I know you only asked about your Photos library so I'll explain how to bring that over alone if that is all you want to do but honestly I'd follow the above advice!!! I assume you have all of your photos in the Photos app on the old computer, you can put a copy of that library on a removable flash drive then once the new Mac is setup, copy the Photos library from the Flash drive to where you want the library to reside. Then to launch Photos and have it use the library you just copied simply double click the library which will launch Photos and begin using the new library. It's that easy!

Mpbuff4 wrote:

I am trying to save all my photos from a iMac (late2013) running Mojave 10.14.6. The iMac runs so slowly that I cannot open iPhoto without it crashing.

That is a bad sign. Although it could be due to other things, the first thing that comes to my mind is "failing hard drive", in which case copying anything off that drive is going to be a bit tricky.

• Do an incremental update of an existing backup (to minimize disk I/O), and what happens to that backup if the failing machine corrupts it?
• Do a full backup to a new, empty disk (to keep your existing backups safe), and you are forcing the Mac that is failing to do even more disk I/O, which might reduce the chances of the new backup succeeding.

What do you have in the way of existing backups of the drive?

If, by any chance, you were using Photos (not the earlier iPhoto), was iCloud Photos enabled?

In other words, are there any safe backups or synchronized copies of your photos that you can work with? Or is it the case that all of your eggs are in one basket: stored internally on a machine whose drive may be failing?

NEVER buy less space on a new Mac than your old Mac. If you have not taken delivery of the new Mac, cancel the order or return it and buy one with adequate storage. Then use method I described in my initial post. If you do not, you stand a chance of losing all of the data on the old Mac.