Data transfer via cable from 2015 iMac to 2019 iMac.

Thunderbolt 2 is backward compatible with Thunderbolt.

Apple Thunderbolt 3 (USB‑C) to Thunderbolt 2 Adapter

Since it is only an adapter you will also need a Thunderbolt cable for the A1419 end. Be sure it is not strictly for Mini-Displayport because that won't work. If in doubt the cable you need is expensive. Displayport cables are cheap.

For reference:

Identify the ports on your Mac - Apple Support

Transfer files between two Mac computers using target disk mode - Apple Support

Comments and a question:

If your Mac won't start, try starting it in "Safe Mode": Start up your Mac in safe mode - Apple Support. Among other actions booting Safe Mode deletes certain cache files maintained by the system, which just might enable you to start the Mac normally, and delete additional files you can cope without.

No Time Machine backup? It would make everything easy.

Apple used "A1419" as an identifier for six different 27" iMacs released between Late 2012 and 2017. The two that came out in 2015 have Thunderbolt 2 ports, with Mini DisplayPort connectors, that run at up to 20 Gbps.

The 21.5" and 27" iMacs that Apple released in 2019 have Thunderbolt 3 ports, with USB-C connectors.

To make a Thunderbolt connection between your Macs, you can use

• Apple Thunderbolt 3 (USB‑C) to Thunderbolt 2 Adapter
• A Thunderbolt 1/2 cable. Such cables have Mini DisplayPort plugs on both ends, but are, or were, built to higher standards than Mini DisplayPort cables. Because Thunderbolt hasn't lived on the Mini DisplayPort connector for many years, such cables may be hard to find and somewhat expensive.

Note that the Thunderbolt 3-to-2 adapter does not transmit power from one side to another, and only works if the devices on each side have their own power supply (which will be the case for your Macs).

Also, Thunderbolt 4 and 5 accessories are not backwards-compatible with Thunderbolt 1 and 2 … the backwards compatibility is limited to other USB-C-based forms of Thunderbolt (see Other World Computing blog article).

P.S. – If you have any bootable clone backups of the old Mac, you could try to start up off one of the backups long enough to free up some space on the internal drive. It would be a lot easier and cheaper than buying Thunderbolt connection hardware.

Booting in Safe Mode is certainly worth trying.

It looks like Apple took away the option to start up in Single User Mode in Mojave and later. That mode is really only appropriate for people accustomed to a Unix command line environment. But it was a tool that could sometimes be useful for recovery – before Apple took it away (presumably in the interests of tightening security).

Mac startup key combinations - Apple Support

Hi,

You can transfer data directly using a Migration Assistant guide and a Thunderbolt 2 cable with a Thunderbolt 3 (USB-C) to Thunderbolt 2 adapter between the 2015 and 2019 iMacs.

What You Need

• 2015 iMac Ports: Thunderbolt 2
• 2019 iMac Ports: Thunderbolt 3 (USB-C)
• Cable & Adapter: An Apple Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter plus a standard Thunderbolt 2 cable.
• Software: Update both Macs to the latest compatible macOS version.

Steps to Transfer

1. Connect the Macs: Plug the Thunderbolt cable into both iMacs using the adapter on the 2019 iMac end.
2. 
   
3. Open Migration Assistant on New Mac: On the 2019 iMac, go to Applications > Utilities > Migration Assistant, select "From a Mac, Time Machine backup, or startup disk", and click Continue.
4. Open Migration Assistant on Old Mac: On the 2015 iMac, open Migration Assistant, select "To another Mac", and click Continue.
5. Confirm the Code: Match the security code displayed on both screens.
6. Select and Transfer: Choose your 2015 iMac on the 2019 iMac, select the files, apps, and user accounts you want to move, and start the transfer.

Thank you for the reply. I guess that would work but as stated the older iMac will not start. Also I am not setting up a newer iMac from the old one.